9780465055692-封面正面.jpg

粗略地看一下整体

情况

A Crude Look

at the

Whole

另见约翰·H·米勒

Also by John H. Miller

复杂自适应系统

Complex Adaptive Systems

 

 

版权所有 © 2015 John H. Miller

Copyright © 2015 by John H. Miller

由 Basic Books 出版，

Published by Basic Books,

 

 

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美国国会图书馆出版品目錄數據

Library of Congress Cataloging-in-Publication Data

米勒，约翰·H·（约翰·霍华德），1959–

Miller, John H. (John Howard), 1959–

粗略地看整体：复杂系统的科学

A crude look at the whole : the science of complex systems

在商业、生活和社会中/约翰·H·米勒。

in business, life, and society / John H. Miller.

页数 厘米

pages cm

包括书目参考和索引。

Includes bibliographical references and index.

ISBN 978-0-465-07386-3（电子书）

ISBN 978-0-465-07386-3 (e-book)

1. 系统分析。2. 系统设计。3. 信息建模。4

. 耦合问题（复杂系统）I. 标题。

1. System analysis. 2. System design. 3. Information modeling.

4. Coupled problems (Complex systems) I. Title.

QA402.M495 2015

QA402.M495 2015

003—dc23

003—dc23

2015027692

2015027692

 

 

10 9 8 7 6 5 4 3 2 1

10 9 8 7 6 5 4 3 2 1

致我的父母

To my parents

插图列表

List of Illustrations

图 2.1     CAPTCHA 挑战

Figure 2.1    A CAPTCHA Challenge

图 2.2    来自规则 30 的模式

Figure 2.2    A Pattern from Rule 30

图 2.3    海螺壳图案

Figure 2.3    A Sea-Snail Shell Pattern

图 2.4    来自规则 22 的模式

Figure 2.4    A Pattern from Rule 22

图 2.5    简单市场的供给与需求

Figure 2.5    Supply and Demand in a Simple Market

图 2.6    一些实验市场的价格

Figure 2.6    Prices Arising in Some Experimental Markets

图3.1     2010年5月6日美国主要市场指数

Figure 3.1    Major US Market Indices on May 6, 2010

图3.2     2010年5月6日E-mini合约价格与成交量

Figure 3.2    The Price and Volume of E-mini Contracts on May 6, 2010

图 4.1    工蜂为蜂巢降温

Figure 4.1    Honeybee Workers Cooling a Hive

图 5.1    一维搜索问题

Figure 5.1    A One-Dimensional Search Problem

图 5.2    使用模拟退火搜索

Figure 5.2    Search Using Simulated Annealing

图 6.1    模拟细菌中的趋化性搜索

Figure 6.1    Chemotaxis Search in a Simulated Bacterium

图 6.2    不相关选择导致的非理性

Figure 6.2    Irrationality Induced by Irrelevant Alternatives

图 7.1    一群蜜蜂

Figure 7.1    A Swarm of Honeybees

图 7.2    群体随时间变化的舞蹈

Figure 7.2    Swarm Dances over Time

图 7.3    最佳选择形成群体的可能性

Figure 7.3    Likelihood of a Quorum Forming for the Best Choice

图 7.4    分散决策中的风险规避

Figure 7.4    Risk Aversion in Decentralized Decision Making

图 7.5    蚂蚁的圆形磨坊

Figure 7.5    A Circular Mill of Ants

图 8.1    莱克兰社区

Figure 8.1    The Community of Lakeland

图 8.2    湖区动态

Figure 8.2    The Dynamics of Lakeland

图 8.3    小世界网络

Figure 8.3    A Small World Network

图 8.4    谢林隔离模型

Figure 8.4    The Schelling Segregation Model

图 9.1    代谢缩放

Figure 9.1    Metabolic Scaling

表 9.1     1820 年至 1945 年战争死亡人数

Table 9.1    Deaths in Warfare, 1820–1945

图 10.1    巴厘岛梯田

Figure 10.1    Balinese Rice Terraces

图 10.2    巴厘岛湖女神祭品

Figure 10.2    Offerings to the Goddess of the Lake, Bali

图 10.3    简单的双状态自动机

Figure 10.3    A Simple Two-State Automaton

图 11.1    沙堆中的自组织临界性

Figure 11.1    Self-Organized Criticality in a Sand Pile

图 12.1     MCMC 青蛙

Figure 12.1    A MCMC Frog

前言

Preface

这些风景中曾经令我焦躁不安的宁静，却日复一日地渗透到我的心中，伴随而来的是一股难以理解的感觉，仿佛我找到了我一直在寻找的东西，却从未发现它到底是什么。

The great stillness in these landscapes that once made me restless seeps into me day by day, and with it the unreasonable feeling that I have found what I was searching for without ever having discovered what it was.

—彼得·马修森，《人类诞生之树》

—Peter Matthiessen, “The Tree Where Man Was Born”

哦在过去的二十年里，我很荣幸能够参与一项伟大的科学事业。这项探索是处于科学的边缘还是前沿，很可能取决于你站在哪里以及你寻找的方向。当我开始走这条路时，我牢记托马斯·品钦的名言：“我们必须寻找老师从未想象过或被鼓励避免的强大道路”，我接受了新的建模方式，利用日益增长的计算能力来解决以前过于复杂而无法分析的问题。我的目标是专注于最初激励我追求科学的大问题，尽管在研究生院及以后不断受到压力，要求将这些研究转向主流范式规定的狭窄道路。

Over the past two decades I’ve had the great pleasure of participating in a wonderful scientific endeavor. Whether this quest is on the fringe or the frontier of science may well depend on where you stand and the direction in which you are looking. When I started down this path, I took to heart Thomas Pynchon’s edict that “we have to look for routes of power our teachers never imagined, or were encouraged to avoid,” and I embraced a new style of modeling that used the ever-growing power of computation on problems that heretofore had been too complex to analyze. My goal was to focus on the big problems that had motivated me to pursue science in the first place, notwithstanding the constant pressure in graduate school and beyond to redirect such inquiries down a narrow path prescribed by the prevailing paradigm.

1988 年，我有幸加入了一小群志同道合的思想家，他们躲藏在新墨西哥州的高地沙漠中。从这样一个不起眼的起点开始，一股新的复杂系统思维浪潮兴起。由于大多数学术机构和科学家在传统范式和领域投入了大量资金，这项新工作一开始很容易被忽视。但事实证明，这种忽视是相当幸运的，因为它让一群不断壮大的富有创造力和才华横溢的科学家（他们每个人都出于某种原因感到需要以不同的方式思考）摆脱了学术机构的束缚，创造了新的科学探究形式和机构，更适合解决世界上的重要问题。我们小组围绕核心思想（如适应性和稳健性）而不是传统的学术领域来制定问题。我们采用了信息时代带来的一套新工具，并开发了新方法，以超越大多数科学家使用的 19 世纪工具箱。我们创建了新形式的学术机构，例如圣菲研究所，它体现了当时正在酝酿的革命思维，使以前孤立的学术领域之间能够轻松交换思想、实例和工具。这一行为非常离谱，以至于传统学术权力忽视了我们的活动，这给了我们必要的时间来完善我们的想法和方法，以便我们能够开始认真挑战现行规范。

In 1988 I was fortunate to join a small group of like-minded thinkers hiding out in the high deserts of New Mexico. From such modest beginnings a new wave of complex-systems thinking emerged. Given the heavy investment of most academic institutions and scientists in traditional paradigms and fields, this new work was easily dismissed at first. This dismissal turned out to be rather fortunate, as it allowed an ever-growing group of creative and talented scientists—each of whom for one reason or another felt the need to think differently—to escape the bounds dictated by the academic establishment and to create new forms of scientific inquiry and institutions better suited to taking on the important problems in the world. Our group formulated problems around core ideas, such as adaptation and robustness, rather than traditional academic fields. We embraced a new set of tools made possible by the information age and developed new methods to move beyond the nineteenth-­century toolbox used by most scientists. We created new forms of academic institutions, such as the Santa Fe Institute, that embodied the revolutionary mind-set that was fermenting, allowing the easy interchange of ideas, examples, and tools across formerly isolated academic fields. The act was outrageous enough that the traditional academic powers ignored our activities, giving us the needed time to refine our ideas and methods so that we could start to seriously challenge the prevailing norms.

在这几年中，复杂系统领域逐渐融合。复杂系统一直是一个超越常规学术界限的领域。然而，在这门浩瀚的科学中，出现了一小部分关键思想，这些思想将成为本书的重点。我自己的兴趣集中在复杂的社会系统上——即由互动的、有思想的（但可能不是聪明的）主体组成的系统——这里介绍的大多数例子都来自这个领域。

In the intervening years, the field of complex systems has had time to coalesce. Complex systems has always been a field that transcends the usual academic boundaries. Yet, across this vast array of science, a small set of key ideas has emerged, and it is these ideas that will be the focus of this book. My own interests center around complex social systems—that is, systems composed of interacting, thoughtful (but perhaps not brilliant) agents—and most of the examples presented here will be drawn from this domain.

由于复杂系统领域正在迅速发展，本书既涉及已知领域，也涉及可能领域。因此，本书讨论的部分工作有长期研究成果作为基础，而其他部分则更具推测性。我希望，这种结合能够传达正在进行的探索的兴奋之情，同时也为复杂系统观点的未来前景奠定基础。当然，任何此类探索必然会是对大量现有思想的选择性探索。

Since the field of complex systems is rapidly evolving, this book is about both the known and the possible. Thus, some of the work discussed here is well grounded in long-standing research efforts, while other parts are of a more speculative nature. My hope is that the combination will convey the excitement of the ongoing quest while also establishing the future prospects for the complex-systems point of view. Of course, any such excursion will, by necessity, be a selective swath through a large field of existing ideas.

本书中讨论的部分研究成果是与 Simon DeDeo、Russell Golman、Steve Lansing、Scotte Page、Tom Seeley、Michele Tumminello 和 Ralph Zinner 过去或正在进行的合作的成果。与 Walter Fontana、Van Savage 和 Geoffrey West 的讨论也对部分材料的完善起到了重要作用。此外，本书中贯穿的各种思想线索都得益于 Phil Anderson、Ken Arrow、Brian Arthur、Bob Axelrod、Ted Bergstrom、Ken Boulding、Jim Crutchfield、Robyn Dawes、Doyne Farmer、Paul Fischbeck、Murray Gell-Mann、John Holland、Erica Jen、Stu Kauffman、Steven Klepper、Blake LeBaron、George Loewenstein、Cormac McCarthy、Norman Packard、Richard Palmer、John Rust、Cosma Shalizi、Carl Simon、Herb Simon、Peter Stadler 和 Hal Varian 的讨论和鼓励。Robert Hanneman、Steve Lansing、Baldomero Olivera、Jacob Peters、Tom Seeley 和 Geoff West 都慷慨地提供了一些研究材料来生成一些图表。Laurence Gonzales 和我的编辑 TJ Kelleher 仔细阅读了手稿，我非常感谢他们两位提出的建议。在本书的最后阶段，Sue Warga 和 Melissa Veronesi 做出了重要贡献。最后，感谢我的经纪人 Jim Levine 对这个项目的支持。

Some of the research discussed in this book is the result of past or ongoing collaborations with Simon DeDeo, Russell Golman, Steve Lansing, Scotte Page, Tom Seeley, Michele Tumminello, and Ralph Zinner. Discussions with Walter Fontana, Van Savage, and Geoffrey West have also been instrumental in refining some of the material. Moreover, the various threads of thought weaving their way throughout this work have benefited from discussions with, and encouragement from, Phil Anderson, Ken Arrow, Brian Arthur, Bob Axelrod, Ted Bergstrom, Ken Boulding, Jim Crutchfield, Robyn Dawes, Doyne Farmer, Paul Fischbeck, Murray Gell-Mann, John Holland, Erica Jen, Stu Kauffman, Steven Klepper, Blake LeBaron, George Loewenstein, Cormac McCarthy, Norman Packard, Richard Palmer, John Rust, Cosma Shalizi, Carl Simon, Herb Simon, Peter Stadler, and Hal Varian. Robert Hanneman, Steve Lansing, Baldomero Olivera, Jacob Peters, Tom Seeley, and Geoff West were all kind enough to provide some of their research materials to generate some of the figures. Laurence Gonzales undertook a careful reading of the manuscript, as did my editor, T. J. Kelleher, and I’m grateful to both of them for their suggestions. During the final stages of the book, Sue Warga and Melissa Veronesi provided key contributions. Finally, thanks to my agent, Jim Levine, for championing this project.

我也很幸运能参与两所杰出的科研机构：卡内基梅隆大学 (CMU) 和圣达菲研究所 (SFI)。这两所机构都有着相同的理念，即寻找极具创造力和智慧的人才，并将他们安置在一个鼓励他们通过跨越常规界限的合作来回答重要问题的环境中，同时尽量减少机构干扰。维持这样的环境很难，我很感谢有远见卓识和创业精神的管理者，比如 SFI 的创始人乔治·考恩，他们创造了这样的学术环境。在 CMU 担任系主任多年后，我认识到让这样的机构正常运转的挑战，我感谢杰里·萨布洛夫 (SFI 总裁)、詹妮弗·邓恩和道格·欧文 (SFI 现任和前任教务长)、马克·卡姆莱特 (CMU 前教务长) 和约翰·莱霍茨基 (CMU 前院长)，他们为让这样的机构正常运转投入了大量精力。 SFI 的其他重要人士也给予了我很大的帮助，包括 Marcella Austin、Patrisia Brunello、Ronda Butler-Villa、Juniper Lovato、Nate Metheny、Ginger Richardson、Janet Rubenstein、Hilary Skolnik、Laura Ware 和 Chris Wood。在 CMU，我领导了社会与决策科学系（即研究互动和深思熟虑的代理人的系），我很感激在匹兹堡期间与我共事的优秀同事。写书和管理部门并不总是兼容的活动，我的业务经理 Sarah Bernardini 在整个过程中一直很亲切，而且很有成效；我感谢她、我的助理 Mary Anne Hunter 以及我的其他工作人员多年来对我的帮助。

I’ve also been fortunate to participate in two remarkable scientific institutions: Carnegie Mellon University (CMU) and the Santa Fe Institute (SFI). Both places have the same ethos, namely, to find incredibly creative and smart people and put them in an environment that encourages answering the important questions by collaborating across the usual boundaries while minimizing institutional distractions. Maintaining such an environment is hard, and I’m thankful for farsighted and entrepreneurial administrators, such as SFI’s founder, George Cowan, who create such academic playgrounds. After a long stint as a department head at CMU, I’ve come to recognize the challenges of making such institutions work, and I’m grateful to Jerry Sabloff (president of SFI), Jennifer Dunne and Doug Erwin (current and former, respectively, chairs of faculty of SFI), Mark Kamlet (former provost of CMU), and John Lehoczky (former dean of CMU), who devote a remarkable amount of energy to making such institutions work. Other key folks at SFI who have been helpful include Marcella Austin, Patrisia Brunello, Ronda Butler-Villa, Juniper Lovato, Nate Metheny, Ginger Richardson, Janet Rubenstein, Hilary Skolnik, Laura Ware, and Chris Wood. At CMU I headed the Department of Social and Decision Sciences (aka the department that studies interacting and thoughtful agents), and I’m grateful for the wonderful group of colleagues who have surrounded me while in Pittsburgh. Writing a book and running a department are not always compatible activities, and my business manager, Sarah Bernardini, has been gracious and productive throughout this process; I’m thankful to her, to my assistant, Mary Anne Hunter, and to my other staff members for their help throughout the years.

最后，感谢我的家人和“Lower-Waldron 公社”，以及我在匹兹堡的朋友和邻居，他们让我能够参与这个非凡而充满活力的社区，这个社区每天都在展示着复杂社会体系的正确目标和美好前景。

Finally, thanks to my family and the “Lower-Waldron Commune,” my friends and neighbors in Pittsburgh, who allow me to participate in a remarkable and vibrant community that demonstrates daily the right purpose and wonderful promise of complex social systems.

JH Miller，

J. H. Miller,

2014 年 8 月，新墨西哥州特苏基

August, 2014, Tesuque, New Mexico

序幕

Prologue

当今的人类就像一个醒着的做梦者，被困在睡眠的幻想和现实世界的混乱之间。大脑寻找但找不到准确的地点和时间。我们创造了一个星球大战文明，有石器时代的情感、中世纪的制度和神一般的技术。我们挣扎求存。我们对自己存在的事实感到非常困惑，这对我们自己和其他生命都是一种危险。

Humanity today is like a waking dreamer, caught between the fantasies of sleep and the chaos of the real world. The mind seeks but cannot find the precise place and hour. We have created a Star Wars civilization, with Stone Age emotions, medieval institutions, and godlike technology. We thrash about. We are terribly confused by the mere fact of our existence, and a danger to ourselves and to the rest of life.

—E.O.威尔逊，《地球的社会征服》

—E. O. Wilson, The Social Conquest of Earth

残酷的事实胜过舒适的幻想。

Better a cruel truth than a comfortable delusion.

—爱德华·艾比

—Edward Abbey

碳复杂性无处不在。

Complexity abounds.

然而，我们传统的科学思维方式依赖于还原论，这种思想既给了我们推动世界发展的阿基米德工具，也给了我们自以为了解自己所做之事的错觉。我们生活在这样一个世界，即使是最简单的部分也能以复杂的方式相互作用，从而创造出一个新兴的整体，其行为似乎与其卑微的起源毫无关联。这是一个既神奇又危险的世界，简单的开端既可能产生奇妙的结果，也可能产生可怕的灾难。

Yet our traditional scientific way of thinking relies on reductionism, an idea that has given us both the Archimedean tools to move the world and the delusion that we understand what we are doing. We inhabit a world where even the simplest parts can interact in complex ways, and in so doing create an emerging whole that exhibits behavior seemingly disconnected from its humble origins. This is at once both a magical and dangerous world, where out of simple beginnings can emerge either a marvelous outcome or an awe-inspiring catastrophe.

就其本质而言，突发事件很容易预测，但很难预测。有时突发事件与我们的需求相吻合。市场可能会创造传递大量关键信息的价格，从而将商品和服务分配到最佳用途。有时突发事件对我们不利。同样的市场可能会不经意间开始相互影响，造成一系列崩溃和预期改变，从而削弱世界经济并影响数十亿人的生活。

By its very nature, emergent behavior is easy to anticipate but hard to predict. Sometimes emergence coincides with our needs. Markets may create prices that transmit a vast array of critical information, resulting in the allocation of goods and services to their best use. At other times emergence works against us. The same markets may inadvertently start to feed on one another, creating a sequence of crashes and altered expectations that cripple a world economy and impact the lives of billions for years.

因此，复杂性无处不在，赋予我们生命和思考能力的复杂力量也让我们能够创建生产系统，但这些系统有时会出现严重错误。令人恼火的是，即使我们试图预测此类故障并建立机制来控制我们的系统，我们也必然会增加系统的复杂性并创造新的故障路径。无论我们试图设计物理系统（如核电站、宇宙飞船或桥梁），还是设计社会系统（如医疗保健、税收政策或食品供应），我们都在创建会以意想不到的方式失败的系统。

So complexity abounds, and the same complex powers that gave us life on earth and the ability to think have also allowed us to create productive systems that, on occasion, go terribly wrong. Maddeningly, even when we try to anticipate such failures and build in mechanisms to keep our systems under control, we necessarily increase the level of complexity in the system and create new paths for failure. Whether we are trying to engineer physical systems, such as nuclear power plants, spaceships, or bridges, or engineer social systems, such as health care, tax policy, or food supplies, we are creating systems that will fail in unanticipated ways.

事实上，认为我们能创造只做好事的复杂系统是一种妄想。话虽如此，运作良好的复杂系统提供了如此多的好处，以至于我们愿意（也应该）接受偶尔的失败。当这些市场运作良好时，与社会获得的无数好处相比，少数市场的暂时性闪电崩盘可能只是个小代价。

Indeed, to think that we might create complex systems that do only good is a delusion. That said, complex systems that work well provide so many benefits that we are (and ought to be) willing to accept some occasional failures. A temporary flash crash across a few markets may be a small price to pay for the countless benefits that accrue to society when those same markets work well.

当复杂性泛滥时，就会有巨龙。尽管如此，遇到你认识的巨龙总比遇到你不认识的巨龙要好。因此，在我们进入超交互世界时，将我们的部分科学事业用于更好地理解复杂系统如何工作（我们希望在此过程中学习如何创建和控制它们）是一项关键投资。为了在这个即将到来的复杂性时代生存下来，我们需要变得积极主动而不是被动应对。为了应对 2010 年的闪电崩盘，美国证券交易委员会在某些市场的股票交易中实施了新的“熔断机制”，但这项政策更多地是出于直觉，而不是科学试验台的洞察力。在 2008 年金融危机之后，我们对银行实施了各种压力测试，试图防止单个银行倒闭，但导致破产的却是整个系统的联系。

When complexity abounds, there be dragons. Nonetheless, it’s better to encounter the dragons you know than the ones you don’t. Thus, devoting some of our scientific enterprise to understanding better how complex systems work—and, we hope, in that process learning how they can be created and controlled—is a critical investment as we advance into a world of hyperinteractivity. To survive this looming age of complexity, we need to become proactive rather than reactive. In response to the flash crash of 2010, the Securities and Exchange Commission implemented new “circuit breakers” in the trading of stocks on some markets, yet this policy was driven far more by intuition than by insights from a scientific test bed. In the wake of the 2008 financial meltdown, we implemented various stress tests on banks to try to prevent an individual bank failure, yet it is the systemwide connections that lead to ruin.

讽刺的是，推动我们这个时代复杂性的计算和通信进步，正是这些工具赋予我们理解甚至驾驭这种复杂性的必要能力。计算机为我们提供了一个观察和试验复杂系统的新窗口。此外，我们新发现的跨越以前无法逾越的距离进行快速通信和协作的能力，可能会加快科学发现和创新所需的步伐。

Ironically, the same computational and communication advances that are driving the complexity of our era are the same tools that may give us the necessary power to understand, and perhaps even harness, that complexity. Computers provide a new window from which to observe and experiment on complex systems. Moreover, our newfound ability to communicate and collaborate rapidly across previously insurmountable distances may accelerate the needed pace of scientific discovery and innovation.

过去，“复杂”一词被用来描述超出我们理解范围的现象，也即超出我们影响范围的现象。科学家（和政客）利用这一标签，轻视社会面临的一些最严重问题，从气候变化到金融崩溃再到恐怖主义。然而，正如后面章节所讨论的，复杂性是自然界的一个方面，可以通过科学分析、理解甚至控制。一旦认识到这一点，就会打开广阔的发现领域，让我们最终理解我们的世界。

In the past, the term complex was used to describe phenomena that were beyond our understanding and, by implication, beyond our ability to influence. This labeling served as a convenient crutch for scientists (and politicians) to dismiss whole swaths of some of the most critical problems facing society, ranging from climate change to financial collapse to terrorism. However, as discussed in the chapters that follow, complexity is an aspect of nature that is amenable to scientific analysis, understanding, and perhaps even control. Once this is recognized, a vast frontier of discovery opens up, allowing us to finally make sense of our world.

我们发现自己正处于一场争夺知识和控制周围复杂世界的竞赛中。如果我们想作为一个物种繁荣发展，甚至生存下去，就必须赢得这场竞赛。我们的生存依赖于将我们的粮食供应、能源网络、全球气候和社会中每个机构联系在一起的复杂系统。我们的规模和连通性已经发展到如此程度，以至于当地的行动现在会产生全球影响。

We find ourselves in a race for knowledge and control of the complex world around us. This is a race that we must win if we are to thrive, and perhaps even survive, as a species. Our very existence relies on the complex systems that bind our food supplies to our energy networks to our global climate to every institution in our society. We have grown to a sheer size and degree of connectivity where local actions now have global consequences.

我们挣扎着，每一次抽搐都可能带来幸福或灾难。

We thrash about, with the potential of emergent bliss or disaster with every twitch.

一

one

简介：真实地点

Introduction: True Places

它不在任何地图上；真实的地方从来都不存在。

It is not down in any map; true places never are.

—赫尔曼·麦尔维尔，《白鲸记》

—Herman Melville, Moby Dick

年代科学就是地图绘制。它把复杂的世界简化为地图上的一些稀疏标记，为穿越原本难以理解且可能充满敌意的地形提供新的指引。好的地图会尽可能地消除虚假信息，以便剩下的信息足以指引我们前进。此外，地图绘制得好，我们就能更深入地了解周围的世界。我们开始认识到河流流向特定方向，城镇不是随机分布的，经济和政治体系与地理环境息息相关，等等。

Science is about mapmaking. It’s about taking a complicated world and reducing it to some sparse set of markings on a map that provides new guidance across an otherwise incomprehensible, and potentially hostile, landscape. A good map eliminates as much spurious information as possible, so that what remains is just enough to guide our way. Moreover, when the map is well made we gain a deeper understanding of the world around us. We begin to recognize that rivers flow in certain directions, towns are not randomly placed, economic and political systems are tied to geography, and so on.

地图和科学往往更多地关乎我们遗漏了什么，而不是我们添加了什么。正如豪尔赫·路易斯·博尔赫斯在他的短篇小说《论科学的精确性》中所述，“制图师行会绘制了一张帝国地图，其大小与帝国大小相同，并且与帝国的点点相符。后代不像他们的前辈那样热衷于制图学研究，他们认为那张巨大的地图毫无用处。”

Maps—and science—are often more about what we leave out than what we put in. As Jorge Luis Borges catalogs in his one-paragraph-long short story “On Exactitude in Science,” “The Cartographers Guilds struck a Map of the Empire whose size was that of the Empire, and which coincided point for point with it. The following Generations, who were not so fond of the Study of Cartography as their Forebears had been, saw that that vast Map was Useless.”

不同的地图（即使是同一景观）也能提供不同的世界观。地形图提供了世界上各种丘陵和山谷的信息，其详细程度刚好足以供徒步旅行者使用。公路地图上稀疏地标出了主要城市及其连接道路，刚好提供了足够的信息供越野驾驶。脱离地图的用途必然会导致挫败感。正确的细节太少，错误的细节太多，都会妨碍我们理解世界的能力。

Different maps—even of the same landscape—provide different insights into the world. A topographic map provides information on the various hills and dales in the world in just enough detail to be useful to a hiker. A road map, with its sparse set of major cities and the roads that connect them, provides just enough information for a cross-country drive. Divorcing a map from its purpose inevitably leads to frustration. Too little of the right kind of detail, or too much of the wrong kind, encumbers our ability to understand the world.

科学的发展离不开对越来越小的现象绘制越来越详细的地图。这种简化策略的核心是希望一旦我们绘制了最小部分的详细地图，我们就可以把马赛克拼凑起来，得到一张有用的博尔赫斯帝国地图。这种策略失败了，虽然结果可能会让博尔赫斯的制图师协会感到高兴，但马赛克就像博尔赫斯设想的那样，是徒劳无功的。

Science has proceeded by developing increasingly detailed maps of decreasingly small phenomena. At the heart of this reductionist strategy is a hope that once we have detailed maps of the smallest of parts, we can paste the mosaic together and have a useful map of Borges’s Empire. That strategy fails, and while the result might please Borges’s Cartographers Guild, the mosaic is as much a fool’s errand as Borges envisioned.

问题不在于我们知识的不完备，而在于还原论的梦想——不，是谬误。还原论失败了，因为即使你对组成一个系统的各个部分了如指掌，你对这些部分在组成整个系统时如何相互作用却知之甚少。对一块玻璃的详细了解并不能帮助你看到并欣赏从彩色玻璃窗中浮现的图像。

The problem lies not in the incompleteness of our knowledge but in the dream—no, the fallacy—of reductionism. Reductionism fails because even if you know everything possible about the individual pieces that compose a system, you know very little about how those pieces interact with one another when they form the system as a whole. Detailed knowledge of a piece of glass does not help you see, and appreciate, the image that emerges from a stained-glass window.

在过去的几十年里，一门新科学正在酝酿之中。这门科学承认，存在着一些基本原则来支配我们的世界，例如涌现和组织，这些原则以各种形式出现在科学的各个角落。例如，在物理学中，单个原子组成磁铁，在生物学中，细胞组成生物体，在经济学中，交易者组成市场。这些原则的普遍性让习惯于以科学学科思考的科学家感到惊讶，而这门新科学必然会超越我们当前学术机构强加的传统界限。在这种科学中，简单的东西产生复杂性，复杂的东西产生简单性。这门科学采用了新的调查工具，例如以计算机为建模基础，以摆脱我们通常使用的科学工具所强加的界限，例如我们今天经常依​​赖的各种数学，这些数学主要源于 17 世纪后期。更根本的是，这门科学挑战了我们的传统观念，即理解来自于将事物分解为最简单的组成部分。

Over the past few decades a new science has been brewing. It is a science that recognizes that there are fundamental principles governing our world—such as emergence and organization—that appear in various guises across all of the nooks and crannies of science. For example, in physics, individual atoms organize into magnets, in biology, cells organize into organisms, and in economics, traders organize into markets. The universality of these principles was a surprise to scientists accustomed to thinking in terms of scientific disciplines, and by necessity, this new science transcends the traditional boundaries imposed by our current academic institutions. It is a science where simple things produce complexity and complex things produce simplicity. It is a science that embraces new investigative tools, such as computers serving as modeling substrates, in order to escape the bounds imposed by our usual collection of scientific tools, such as the various pieces of mathematics, largely derived in the late 1600s, that we so often rely on today. More fundamentally, it is a science that challenges our traditional notion that understanding comes from reducing things to their simplest components.

可惜，我们所追求的新科学，即可能左右我们生活和命运的关键方面的科学，正如赫尔曼·梅尔维尔所说，“并不在任何地图上；真实的地方从来都不存在。”目前实践的科学——心理学与经济学分离，物理学与生物学分离，等等——已经取得了显著的成果。科学思想的创造性破坏，以及其通过公开披露、评估和纠正思想来定义边界的内在追求，为我们提供了洞察力的引擎。然而，代价是各个领域在智力上越来越相互分离。精确观察世界的一小部分已经成为学术规范，几乎完全取代了我圣菲研究所同事默里·盖尔曼所说的“粗略观察整体”。

Alas, the new science we are after, the one that may hold sway over critical aspects of our life and destiny, is, as Herman Melville says, “not down in any map; true places never are.” Science as currently practiced—with psychology separate from economics, physics separate from biology, and on and on—has been remarkably productive. The creative destruction of scientific ideas, with its inherent quest to define the frontier by publicly disclosing, evaluating, and correcting ideas, has provided us with an engine of insight. The cost, however, is that individual fields have become increasingly separated from one another intellectually. Taking an exact look at a small piece of the world has become the academic norm and has almost fully displaced taking what my Santa Fe Institute colleague Murray Gell-Mann calls “a crude look at the whole.”

这似乎是一个小问题，但当我们真正想探索的地方时，我们就会发现它的重要性。以任何全球性的社会挑战为例，比如金融崩溃、气候变化、恐怖主义、流行病、革命或社会变革：没有一个与任何特定的学术领域完全吻合。而且，即使有，还原论的方法仍然可能无法让我们理解整体。复杂性的基本原理描述了即使是简单的部分，一旦组合在一起，似乎也会有自己的生命。比如说，对发动机的每个部件、每个螺栓、活塞、凸轮等都有深入的了解，并不能告诉我们当我们把这些部件放在一起并开始相互作用时会发生什么。此外，如此深入的了解如果我们增加某个气缸的尺寸，现有知识无法让我们洞悉整个发动机会发生什么情况。

That may seem a minor problem, but we see its importance when we look at the true places we wish to explore. Take any global-scale, societal challenge, such as financial collapse, climate change, terrorism, epidemics, revolution, or social change: not one neatly aligns with any particular academic field. Moreover, even if one did, the reductionist approach still may not let us understand the whole. The fundamental principles of complexity describe how even simple parts, once together, seemingly take on a life of their own. Having intimate knowledge of, say, each part of an engine, every bolt, piston, cam, and so on, tells us little about what happens when we put those pieces together and they begin to interact with one another. Moreover, such intimate knowledge gives us no insight into what would happen to the engine as a whole if, say, we increase the size of one of the cylinders.

简化并不能让我们深入了解构造。而构造中却充满了复杂性。

Reduction gives us little insight into construction. And it is in construction that complexity abounds.

从集市到变形虫，从蜜蜂到大脑，从城市到崩溃，再到斑马条纹，我们周围的世界是一个复杂的百科全书。有时，这种复杂性是由进化等自然力量塑造的，比如从我们大脑中产生的意识。有时，我们参与了它的创造，比如从商品交易大厅中看似混乱的噪音和手势中产生的稳定价格流。如果没有复杂系统科学，我们就几乎没有机会理解，更不用说塑造我们周围的世界了。

From agoras to amoebas, from bees to brains, from cities to collapse, and on up to zebra stripes, the world around us is an encyclopedia of complexity. Sometimes this complexity arises shaped by natural forces such as evolution, as in the consciousness that emerges from our brains. At other times we have a hand in its creation, as in the steady stream of prices that arises from the seemingly chaotic noise and gestures in a commodities trading pit. Without a science of complex systems, we have little chance to understand, let alone shape, the world around us.

复杂系统的首次学术讨论至少可以追溯到 1776 年，当时亚当·斯密在《国富论》中简要讨论了“看不见的手”，认为它是一种力量，可以引导自私自利的交易者做出无意的、符合社会期望的结果。当然，基于看不见的手的科学命题更像是对神的祈求，而不是科学理论，它对经济学家的用处，就如同拉迪亚德·吉卜林的“恰如其分”的故事对试图解释豹子如何长出斑点的生物学家的用处一样。

The initial academic discussions of complex systems can be traced back to at least 1776, when Adam Smith, in his Wealth of Nations, briefly discusses the “invisible hand” as a force that leads self-interested traders to unintentional, socially desirable outcomes. Of course, scientific propositions that are based on an invisible hand are more akin to the invocation of a deity than to a scientific theory and are about as useful to an economist as one of Rudyard Kipling’s just-so stories is to a biologist trying to explain how a leopard gets its spots.

现代复杂系统思维运动可以追溯到原子时代和信息时代的开端，当时斯坦尼斯拉夫·乌拉姆和约翰·冯·诺依曼利用世界上第一批可编程电子计算机，开始模糊传统学术领域之间的界限，因为他们正在研究诸如机器是否真的可以自我复制等问题。在这种努力下，出现了一类模型，这些模型从一组简单、定义明确的部件和相互作用开始，产生了一组令人惊讶的丰富的全局模式。

The modern movement of complex-systems thinking can be tied to the beginnings of the atomic and information ages, when scientists such as Stanislaw Ulam and John von Neumann, using some of the world’s first programmable electronic computers, began to blur the lines between traditional academic fields as they pursued questions such as whether a machine could be truly self-reproducing. Out of this effort arose a class of models that, starting with a collection of simple, well-defined pieces and interactions, results in a surprisingly rich set of global patterns.

对这些图案的研究不仅有助于我们了解动物斑纹的用途（例如伪装），还有助于我们了解斑纹的形成原因。豹子的 DNA 中是否一定存在某种总体规划，决定了皮肤上每个位置的颜色，就像数字图像文件决定计算机显示器上每个像素的颜色一样？或者，是否有更普遍的解释可以告诉我们豹子身上的斑点是如何形成的？

The study of those patterns was an important step toward understanding not just the purpose of an animal’s markings—say, camouflage—but also how they arise. Is it necessary that there be some master plan contained within the DNA of a leopard that specifies the color of each location on its skin, similar to how a digital image file directs the color of each pixel on a computer display, or is there a more universal explanation that can tell us how a leopard gets its spots?

乌拉姆和冯·诺依曼开创的简单数学和计算模型为我们提供了一个观察这种复杂性起源的视角。我们发现，简单部分的组合，在局部相互作用，足以导致与其起源完全不同的整体行为。因此，豹子如何获得其斑点——或者低等（但危险）的海蜗牛如何获得其壳图案，甚至交易大厅的嘈杂声如何导致一套井然有序的交易和价格——的可能答案比我们想象的要简单得多，更普遍，也更令人着迷。

The simple mathematical and computational models begun by Ulam and von Neumann have given us a lens through which to look at the origins of such complexity. We find that the combination of simple pieces, locally interacting with one another, is sufficient to lead to global behavior that is rather alien to its origins. Thus, the likely answer to how the leopard gets its spots—or how a lowly (but dangerous) sea snail gets its shell pattern, or even how the cacophony of a trading pit results in a well-organized set of trades and prices—is at once far simpler, far more universal, and far more fascinating than we might imagine.

在过去的几十年里，对相互作用系统的研究为我们理解复杂系统开辟了新的领域。无论我们考虑的是计算机中以光速运行的抽象模型，还是一个世纪以来水稻种植的精心整理的人类学证据，一小套控制复杂系统的核心原则都已出现。相互作用系统在代理之间形成反馈回路，这些回路驱动着系统的行为。这种反馈会根据代理之间的异质性程度而得到缓和或加剧。相互作用系统也往往天生就充满噪声，这种随机性可能会产生令人惊讶的全球后果。当然，谁与谁相互作用是这些系统的基本属性，这种相互作用网络是复杂系统的基本要素。

Over the last few decades, the study of interacting systems has opened up a new frontier in our understanding of complex systems. Whether we consider abstract models running at the speed of light inside a computer or the carefully curated anthropological evidence of a century of rice farming, a small set of core principles governing complex systems has emerged. Interacting systems develop feedback loops among the agents, and these loops drive the system’s behavior. Such feedback is moderated or exacerbated depending on the degree of heterogeneity among the agents. Interacting systems also tend to be inherently noisy, and such randomness can have surprising global consequences. Of course, who interacts with whom is a fundamental property of these systems, and such networks of interaction are an essential element of complex systems.

反馈、异质性、噪声和网络等核心原则可用于理解复杂性的新层面。例如，有些复杂系统（如您的大脑）以完全分散的方式做出连贯而富有成效的决策，似乎不受控制。其他系统面临着深层次的限制，例如将氧气输送到您体内的所有细胞，这导致了缩放定律，这些定律可以将看似不相连的世界部分按照简单的关系排列起来。而其他系统（如社会运动的成员）会自组织进入临界状态，开始表现出共同的特征行为。许多交互系统在代理之间发展合作，复杂行为一旦出现，就允许主体进入一个新的机会领域，我们现在可以理解这种转变。最后，通过重新利用在现代复杂系统科学初期首次开发的方法和思想，我们可以生成关于自适应系统行为的新定理。

Core principles such as feedback, heterogeneity, noise, and networks can be used to understand new layers of complexity. For example, there are complex systems, such as your mind, that generate coherent and productive decisions in a completely decentralized manner, seemingly without control. Other systems, facing deeply embedded constraints such as getting oxygen to all of the cells in your body, lead to scaling laws that can take seemingly disconnected parts of the world and align them along a simple relationship. Yet other systems, such as the members of a social movement, self-organize into critical states that begin to exhibit a common characteristic behavior. Many interacting systems develop cooperation among the agents, a complex behavior that, once arisen, allows agents to shift into a new realm of opportunity, and we are now in a position to understand such a transition. Finally, by repurposing methods and ideas that were first developed at the dawn of the modern science of complex systems, we can generate a new theorem about the behavior of adaptive systems.

这些推动复杂系统的核心原理及其在理解新复杂性层面中的应用是下文的重点。

These core principles driving complex systems, and their application to understanding new layers of complexity, are the focus of the pages that follow.

互动的一个重要方面是反馈。有时反馈可以稳定系统，例如当我们安装一个不太敏感的恒温器来控制炉子时。其他时候反馈会导致系统失控，例如当我们将麦克风放得太靠近扬声器时，会产生越来越大的刺耳声音。最近市场互联互通的增长导致系统充斥着反馈。这是通过新的通信链接、衍生证券的兴起以及高速计算机自动交易的使用实现的。事实上，这些变化很容易就超出了我们真正理解其影响的能力，金融市场已成为一项无意的普罗米修斯实验，我们现在的经济生活就是建立在它之上的。

One critical aspect of interactions is feedback. Sometimes feedback stabilizes the system, as happens when we install a not-too-touchy thermostat to control the furnace. Other times feedback causes a system to go out of control, as happens when we place a microphone too close to a loudspeaker, producing an ever-increasing screech. The recent growth of market interconnectivity has resulted in a system rife with feedbacks. This has come about through new communication links, the rise of derivative securities, and the use of high-speed, computer-automated trading. Indeed, these changes have easily outpaced our ability to truly understand their implications, and financial markets have become an unintentional Promethean experiment upon which we now base our economic livelihood.

一个例子是 2010 年 5 月 6 日的“闪电崩盘”，当时堪萨斯州堪萨斯城郊区的一台交易计算机的编程出现了简单的疏忽，导致全球市场暂时崩溃。随后发生的灾难导致主要股票指数的价格发生剧烈波动，并导致以前价值不菲的支柱公司的股票以低价出售（请注意，不是一美元的几分之一，而是几分之一美元）。幸运的是（而且非常了不起），危机发生十五分钟后暂停五秒钟的交易足以开始恢复系统，市场又回到了更熟悉的模式。

An example is the “flash crash” of May 6, 2010, when a simple oversight in the programming of a trading computer in a suburb of Kansas City, Kansas, caused a temporary collapse of global markets. The havoc that ensued resulted in dramatic price changes on key stock indices and caused the shares of previously valuable mainstay companies to be sold for pennies (not pennies on the dollar, mind you, but pennies). A five-second trading pause invoked fifteen minutes into the crisis was, fortunately (and remarkably), sufficient to begin to restore the system, and the markets settled back into a more familiar pattern.

2008 年发生了一起规模更大的事件，导致金融海啸席卷全球经济，影响了数十亿人的生活，至今仍困扰着我们。研究这场危机，我们发现，经济领域中的任何一个参与者，从房主到抵押贷款经纪人再到评级机构，都在做出明智的决定，但这些参与者之间的联系却产生了一系列不幸的反馈循环，注定了整个系统会崩溃。

In 2008 a much larger event happened that resulted in a financial tsunami that rolled across the world’s economy, affecting the lives of billions and plaguing us to this day. Examining this crisis, we find a situation where any single agent on the economic landscape, from homeowners to mortgage brokers to rating agencies, was making sane decisions, yet the connections among these agents created a series of unfortunate feedback loops that destined the system to fail.

2008 年的经济崩溃代表着经济学界的重大失败。经济学家们不仅未能预见到即将到来的冲击，而且危机爆发后，他们也不知道该如何应对。这种失败的部分原因可以归结于还原论者希望将事物分解为简单的部分。用现代经济理论的语言来说，这导致了对“代表性代理”的依赖，这种结构试图利用一个超级消费者来捕捉所有消费者的行为。在某种程度上，这种选择源于 14 世纪修士奥卡姆的威廉神父的指示，即倾向于使用更简单的解释而不是更复杂的解释。当然，奥卡姆仍然要求模型，无论复杂与否，都要解释我们想要了解的内容。实际上，使用代表代理的决策也受到经济学家通常使用的建模工具的局限性的影响，因为这些工具只有在系统具有高度同质性的情况下才能部署。

The economic collapse of 2008 represents a major failure for the profession of economics. Not only did economists fail to see the onslaught coming, but once the crisis arose, they had no idea how to deal with it. Part of this failure can be traced to the reductionist desire to break things down to simple parts. In the language of modern economic theory, this led to a reliance on “representative agents,” constructs that attempt to capture the behavior of, say, all consumers using a single megaconsumer. In part, such a choice arises from the fourteenth-century friar Father William of Ockham’s dictate to prefer simpler explanations to more complicated ones. Of course, Ockham still requires that the model, complicated or not, explain what we want to understand. In reality, the use of representative agents is also driven by the limitations of the modeling tools typically used by economists, as these tools can be deployed only if there is a high degree of homogeneity in the system.

虽然同质性是一个有用的假设——出于哲学和实践原因——但复杂系统的研究表明，异质系统的行为可能不那么容易被平均化。无论是我们观察蜜蜂蜂巢的温度控制还是暴乱的可能性，异质系统通常以不同于同质系统的方式运作。

While homogeneity is a useful assumption—for both philosophical and practical reasons—the study of complex systems suggests that the behavior of heterogeneous systems may not be so easily averaged out. Whether we are looking at the temperature control of a honeybee hive or the likelihood of a riot, heterogeneous systems often function in ways that are different from homogeneous ones.

认识到异质性不仅会改变我们对系统行为方式的预测，还会改变我们的政策处方。同质系统往往会经历快速变化和震荡，而异质系统的反应往往较慢。因此，你发起或镇压社会运动的能力与参与其中的人的异质性程度有关。同样，市场可能需要交易者之间存在一定的异质性才能保持稳定。

Recognizing heterogeneity not only changes our predictions about how a system will behave but also alters our policy prescriptions. Homogeneous systems tend to undergo rapid changes and oscillations, while heterogeneous ones tend to react more slowly. Thus, your ability to start, or quash, a social movement is tied to the degree of heterogeneity among the people involved. Similarly, markets may require some heterogeneity among the traders to remain stable.

复杂系统通常具有某种程度的随机性，这些随机性与代理的行为或交互结构有关。也许令人惊讶的是，这种随机性可能很有用。我们常常害怕系统中的随机性。事实上，现代企业管理的一个关键原则是通过消除系统中所有随机性来源来追求质量。任何过程都是如此。鉴于这样的必要性，人们很容易将随机性视为需要对抗的敌人，而不是可以把握的机会。但复杂性研究表明情况并非如此。随机性是达尔文进化论的基础，该理论依赖于这样的观点：繁殖过程中的错误（变异）将为选择提供素材，并产生“最美丽、最奇妙的无穷形式”。

Complex systems often have some inherent degree of randomness tied to the behavior of the agents or the structure of interactions. Perhaps surprisingly, such randomness can be useful. We often dread randomness in systems. Indeed, a key dictate in modern business management is to seek quality by removing all sources of randomness from any process. Given such imperatives, it is easy to think of randomness as a foe to be fought rather than as an opportunity to be embraced. The study of complexity suggests otherwise. Randomness is fundamental to Darwin’s theory of evolution, which relies on the notion that errors (variations) during reproduction will provide grist for the mill of selection and result in “endless forms most beautiful and most wonderful.”

达尔文的理论以及其中随机性的作用，实际上是关于在崎岖地形上发现。我们发现新机遇（无论是新形式的动物还是新技术）的能力，与地形的崎岖程度和我们的搜索技巧息息相关。在简单的地形上，即使是简单的搜索也能找到好的结果。在崎岖的地形上，这样的搜索就会失败。

Darwin’s theory, and the role of randomness therein, is really about discovery on rugged landscapes. Our ability to discover new opportunities, whether new forms of animal life or novel technologies, is tied to both the ruggedness of the underlying landscape and our search skills. On simple landscapes, even simple searches can find good outcomes. On rugged landscapes, such searches founder.

景观变得更加崎岖，因为组成景观的元素相互作用更加频繁。假设我们正在寻找一种新型药物鸡尾酒来对抗某种疾病。如果我们添加到混合物中的每种药物都有独立于其他药物的效果，那么我们只需一次添加一种药物并只保留那些可以提高鸡尾酒整体疗效的药物，就可以快速找到最佳鸡尾酒。然而，如果药物之间相互作用，这种简单的搜索策略就会失效，因为各种相互作用不再提供关于如何最好地进行的明确信号。

Landscapes become more rugged as the elements that compose them interact more. Suppose we are seeking, say, a novel drug cocktail to fight some disease. If each drug we add to the mix has an effect that is independent of the others, then we can quickly find the best cocktail just by adding the drugs one at a time and keeping only the ones that improve the cocktail’s overall efficacy. However, if the drugs interact with one another, this simple search strategy breaks down, as the various interactions no longer provide a clear signal on how best to proceed.

事实证明，引入随机性可以大大提高我们在崎岖地形中搜索的能力。正如詹姆斯·乔伊斯所说，“错误……是“发现”。正如进化依靠变异来发现大多数奇妙的形式一样，在搜索中引入错误可以成为一种强有力的发现策略。

It turns out that the introduction of randomness can greatly improve our ability to search on rugged landscapes. As James Joyce noted, “Errors . . . are the portals of ­discovery.” Just as evolution relies on variation to uncover most wonderful forms, introducing errors into a search can be a powerful strategy for discovery.

接受系统中的随机性会迫使我们放弃一些控制权。然而，当我们面临难题时，如果我们想改善结果，这可能是正确的做法。更普遍地说，精心控制的集中式系统可能更像是一种现代产物，受还原论思维的驱动，而不是一种普遍规范。事实上，有很多例子表明，反馈、异质性和随机性的原则共同创造了没有集中控制但非常高效的复杂系统。有效的分散决策可能是从复杂系统中涌现出的最好的新旧思想之一。

Accepting randomness in a system forces us to give up some control. Yet when we are facing hard problems, this may be the right thing to do if we want to improve the outcome. More generally, it may be the case that carefully controlled, centralized systems are more of a modern artifact, driven by reductionist thinking, than a universal norm. Indeed, there are plenty of examples where the principles of feedback, heterogeneity, and randomness conspire to create complex systems that are without centralized control, yet quite productive. Effective decentralized decision making may be one of the best new old ideas to emerge from complex systems.

当我们思考决策时，我们自然倾向于关注我们自己的决定。在过去的几十年里，整个学术领域都致力于理解人类如何做出决定。虽然揭开我们决策大脑的奥秘是一项值得的事业，但我们很容易忽视生物世界其他地方发生的大量决定。举一个例子，细菌生活在含有有用和有害化学物质的环境中，因此它们必须不断做出生死攸关的决定，决定搬到哪里，权衡各种机会。没有大脑，这怎么可能呢？更有趣的是，人类（大概使用大脑）和细菌（大概不使用一个）在简单的实验中展示类似的选择错误模式。

When we think about decision making, our natural tendency is to focus on our own decisions. Over the last few decades entire academic fields have been devoted to understanding how humans make decisions. While unraveling the mysteries of our deciding brain is a worthy enterprise, it is far too easy to overlook the vast number of decisions that take place elsewhere in the biological world. To take just one example, bacteria exist in environments that contain both useful and harmful chemicals, and thus they constantly must make life-and-death decisions about where to move, given the trade-offs among various opportunities. How is this possible without a brain? Even more intriguing, humans (presumably using a brain) and bacteria (presumably not using one) demonstrate similar patterns of choice errors in simple experiments.

无需大脑也能做出正确决定这一观点令人震惊。从单个细菌到大型社会系统（如蜂巢和金融市场），决策无处不在。一群蜜蜂如何做出正确决定？蜂后不是领导者。她过着一种相当孤立的生活，就像一台精心照料的产卵机器，只能发出有关其健康和存在的信号，而不是向蜂巢的其他成员发出操作指令。

The notion that one doesn’t need a brain to make good decisions is startling. From the lone bacterium on up to large-scale social systems such as honeybee hives and financial markets, we are surrounded by decision making. How can a swarm of honeybees make good decisions? The queen is not the leader. She leads a rather insular life, serving as a well-tended egg-laying machine, able to emit only signals about her health and existence, rather than operating instructions to the rest of the hive.

卡尔·冯·弗里施 (Karl von Frisch) 在 20 世纪 40 年代末发现了蜜蜂的交流方式，这启发了一代又一代的科学家对蜜蜂的行为进行仔细的观察和分析。通过这项工作，我们开始了解一个蜂群如何在没有任何中央领导的情况下挑选出各种选择并做出正确的决定。对于一个蜂群来说，一个特别重要的决定——它是延续还是消亡——是在旧位置变得过于拥挤时寻找新的位置。

Karl von Frisch’s discoveries about honeybee communication in the late 1940s inspired generations of scientist to undertake the careful observation and analysis of honeybee behavior. Through this work, we are beginning to understand how a colony can sort out its various options and make good decisions without any central leadership. One particularly important decision for a colony—the difference between its perpetuation and demise—is finding a new location when the old one becomes too crowded.

一群蜜蜂通过使用一些简单的规则和反馈机制来解决寻找新地点的问题。侦察蜂在确定一个潜在的新地点后，会向其他侦察蜂宣传。地点越好，侦察蜂宣传得越积极。这种分散的过程使蜜蜂能够对地点进行分类和适当调查，最终导致蜂群倾向于相对快速地选择最佳地点，而无需任何中央指导。

A swarm of bees solves the problem of finding a new location through the use of a few simple rules and feedback mechanisms. Scout bees, after identifying a potential new site, advertise it to other scouts. The better the site, the more vigorously the scout promotes it. This decentralized process allows the sites to be sorted out and suitably investigated, and ultimately it results in the swarm tending to choose the best site relatively quickly without any central direction.

了解这种分散的过程有许多好处。它解决了蜜蜂自然史中一个有趣的、生死攸关的案例。它还展示了如何使用分散机制来解决难题。这表明我们可以劫持一种方法，供自己使用，比如协调计算机网络或大型人类组织。最后，也许最深刻的是，这种分散机制让我们对相关现象有了新的认识。例如，蜜蜂之于神经元可能就像蜂巢之于大脑。群体决策是否类似于人类意识？

Understanding such decentralized processes has numerous benefits. It solves an interesting, life-or-death case of honeybee natural history. It also shows how decentralized mechanisms can be used to solve hard problems. This suggests an approach that we might be able to hijack for our own use in, say, coordinating computer networks or large-scale human organizations. Finally, and perhaps most profoundly, such decentralized mechanisms give us new insights into related phenomena. For example, perhaps bees are to neurons as hives are to brains. Are swarm decisions akin to human consciousness?

复杂性出现在相互作用的代理系统中。将一些行为简单的代理以特定方式连接在一起，就会产生一些全局行为。改变连接，通常会产生新的全局行为。鉴于此，了解交互模式（即网络）如何影响行为是理解复杂系统的基础。

Complexity arises in systems of interacting agents. Take some agents with simple behavior, connect them together in a particular way, and some global behavior will result. Alter the connections and, often, new global behavior arises. Given this, knowing how patterns of interactions—that is, networks—influence behavior is fundamental to understanding complex systems.

即使是在湖边邻居相互竞争以跟上彼此步伐的简单模型中，有趣的模式也开始出现。从这样一个简单的系统开始，我们可以稍微改变连接，并发现完全不同的行为占主导地位。事实上，通过只引入几个长距离连接，我们发现它毕竟可能是一个小世界，任何人都可以通过几个中介与其他人建立联系。如果邻居可以相互连接，他们就可以相互影响。因此，定义邻里的网络驱动着整个系统的行为。这是行为往往令人惊讶。例如，一个混合良好的世界，邻居之间相互容忍，很容易分裂成同质类型的社区。

Even in simple models such as lakeside neighbors competing to keep up with one another, interesting patterns begin to emerge. Starting from such a simple system, we can alter the connections slightly and find radically different behavior taking over. Indeed, by introducing only a few long-range connections, we find that it may be a small world after all, where anyone can connect to anyone else using only a few intermediaries. If neighbors can connect to one another, they can influence one another. Thus, the networks that define neighborhoods drive system-wide behavior. This behavior is often surprising. For example, a well-mixed world where neighbors are tolerant of others easily segregates into neighborhoods of homogeneous types.

从大量存在的复杂性中得出的一个更令人惊讶的原则是缩放定律的存在。从 19 世纪末开始，生物学家开始注意到，当适当缩放时，各种生物的各种物理和生理特征会以简单的方式排列。一个简单的规则将单细胞的新陈代谢与蓝鲸的新陈代谢联系起来。知道一只老鼠的心率和体重，我们就可以预测一头重达一千磅的牛的心率。做出这种预测的能力与控制这种复杂系统的基本约束有关。在这种情况下，我们为生物体提供资源所需的通路的密度限制推动了缩放。

One of the more surprising principles coming out of the complexity that abounds is the existence of scaling laws. Starting in the late 1800s, biologists began to notice that, when appropriately scaled, various physical and physiological features of a variety of organisms aligned in a simple way. A simple rule links the metabolism of a single cell to that of a blue whale. Knowing the heart rate and weight of, say, a mouse allows us to predict the heart rate of, say, a thousand-pound cow. The ability to make such predictions is tied to the fundamental constraints that govern such complex systems. In this case, limits on how densely we can pack the pathways needed to provide resources to the organism drive the scaling.

缩放定律也出现在其他复杂系统中。城市或公司的规模往往遵循明确的定律，最大的城市或公司的规模是第二大城市的两倍，是第三大城市的三倍，依此类推。同样，在一本书中，最常用的单词出现的可能性是下一个最常用单词的两倍。甚至战争的次数和死亡人数也受缩放定律的支配。

Scaling laws arise in other complex systems as well. The size of cities or firms tends to follow well-defined laws, with the largest having twice the size of the second-largest, three times that of the third-largest, and so on. Similarly, in a book, the word that is most commonly used is twice as likely to occur as the next most commonly used word. Even the number and death tolls of wars are governed by a scaling law.

了解支配我们生活的尺度定律为我们的未来打开了一扇大门。例如，在过去的一个世纪里，我们看到了城市化的趋势。如今，​​全球一半以上的人口都居住在城市地区。这种趋势对人类来说是好是坏？这个问题的答案与城市各种尺度定律的系数有关。这些系数将告诉我们，更多的城市化是否会让我们使用更少的资源、更具创造力等等。同样，战争的尺度定律可能暗示着未来我们可能会看到多少冲突和多少死亡。

Knowing the scaling laws that govern our lives provides a portal into our future. For example, over the last century we have seen a trend toward urbanization. More than half of the world’s population now lives in urban areas. Is such a trend good or bad for humanity? The answer to this question is tied to the coefficients of various scaling laws of cities. These will tell us whether more urbanization will allow us to use fewer resources, be more inventive, and so on. Similarly, the scaling laws of wars may hint at how many conflicts with how many deaths we are likely to see in the future.

在复杂的社会系统中，我们经常看到合作的出现。系统中的代理可以相互竞争或合作。竞争会让你略微好一点，而合作会让你好很多。不幸的是，大多数社会系统的激励机制至少对个人而言更倾向于竞争而不是合作。这样的系统很容易最终导致较差的竞争结果。

In complex social systems we often see the emergence of cooperation. Agents in systems can either compete or cooperate with one another. Competition makes you slightly better off, while cooperation makes you much better off. Unfortunately, most social systems have incentives that favor, at least individually, competition over cooperation. Such systems can easily end up with the inferior, competitive outcome.

尽管存在竞争而非合作的动机，复杂的社会系统仍可能找到实现合作和社会优越结果的方法。在巴厘岛，农民们已经可持续地耕种风景如画的梯田一千多年了。尽管相互竞争稀缺水源的经济动机似乎势不可挡，但这种合作仍在继续。然而，通过仔细解开控制这一生态系统的复杂动态，并应用上面讨论的反馈和网络原则，我们可以解决这个明显的异常现象。奇怪的是，破坏性农作物病虫害的出现所带来的邻里反馈重新调整了每个农民的激励共享水资源，通过这种共享，社会变得更好。此外，协调种植的新需求为复杂的宗教机构开辟了空间，各种神殿和寺庙都与灌溉系统相连。

Notwithstanding incentives to compete rather than cooperate, complex social systems may find ways to achieve the cooperative and socially superior outcome. On the island of Bali, farmers have been farming the picturesque rice terraces sustainably for more than a thousand years. This cooperation persists despite what would appear to be overwhelming economic incentives to compete with one another for the scarce water. However, by carefully unraveling the complex dynamics that govern this ecosystem and applying the principles of feedback and networks discussed above, we can resolve this apparent anomaly. Oddly, the neighborhood feedbacks from the presence of damaging crop pests and diseases realign each farmer’s incentive to share water, and with such sharing, society is better off. Moreover, the newfound need for coordinated cropping opens up a niche for an elaborate religious institution with various shrines and temples tied to the irrigation systems.

我们还可以制定一个抽象模型，从中观察和理解合作的出现和持续。我们发现，在一个充满敌意的世界里，竞争很容易压倒整个系统，竞争策略的细微变化为合作的出现提供了手段。合作主体发展出一种沟通方式，以便相互识别。通过这样做，他们获得了合作的好处，同时在遇到竞争主体时将损失降到最低。通过这样的机制，合作可以出现并持续下去。

We can also formulate an abstract model from which we can observe and understand the emergence and persistence of cooperation. We find that in a world red in tooth and claw, where competition can easily overwhelm the system, slight variations in competitive strategies provide a means by which cooperation can emerge. Cooperative agents develop a way to communicate so as to recognize one another. By doing so, they get the benefits of cooperation while minimizing losses when they encounter competitive agents. Through such a mechanism, cooperation can emerge and be sustained.

我们将要探讨的最后一个原则是自组织临界性。想象一下，沙粒慢慢地堆积在桌子上。当我们扔下每一粒沙粒时，它可能会落在一个稳定的地方，使沙堆变大，但这样做会使那个地方比以前更不稳定。或者，它可能会落在沙堆不稳定的部分，引发雪崩。

The final principle we will explore is that of self-­organized criticality. Consider grains of sand being slowly piled on a table. As we drop each grain, it might land on a stable spot and increase the pile, but in doing so it makes that spot less stable than it was before. Alternatively, it might land on an unstable part of the pile, triggering an avalanche.

随着时间的推移，这种稳定性和不稳定性相互作用使沙堆自发进入临界状态。一旦发生这种情况，我们发现各种规模的雪崩都有可能发生（其分布由标度定律描述），小型雪崩发生的可能性远大于大型雪崩。

Over time, this interplay of stability and instability self-organizes the sand pile into a critical state. Once this happens, we find that avalanches of all sizes are possible (the distribution of which is described by a scaling law), with smaller ones far more likely than larger ones.

沙堆的一个含义是，一旦我们进入临界状态，一粒沙子的掉落，在极少数情况下，都可能导致一场雪崩，席卷整个整个沙堆。各种社会系统可能会向类似的临界状态发展。我们可能会发现自己处在一个由沙堆数学统治的世界。随着典型的世界事件发生，股票市场可能会受到许多常规调整。然而，这些相同类型的事件在极少数情况下会导致大规模的重新调整。文明可能由倾向于将人们推向临界状态的政治体系所统治，在这种情况下，小事件偶尔会导致古代文明的崩溃，或者正如我们在阿拉伯之春中看到的那样，现代政府的崩溃。

One implication of the sand pile is that once we enter the critical regime, the dropping of a single grain of sand can cause, on rare occasions, an avalanche encompassing the entire pile. Various social systems may evolve toward similar critical states. We might find ourselves in a world governed by the mathematics of the sand pile. Stock markets may be subject to numerous routine adjustments as typical world events transpire. Yet these same types of events will, on rare occasions, lead to a massive readjustment. Civilizations may be governed by political systems that tend to push people toward critical states, where small events occasionally result in the collapse of an ancient civilization or, as we saw in the Arab Spring, modern governments.

我们将沿着一条线索来结束对复杂性的探索，这条线索始于我们在原子和信息时代之初想要了解原子相互作用的愿望，终于复杂自适应系统的新基本定理。20 世纪 50 年代初，尼古拉斯·梅特罗波利斯 (Nicholas Metropolis) 和其他人开发了一种算法来探索相互作用的分子系统。该算法的核心是一组简单的操作，最终可以让人们恢复无法直接生成的关键信息；就像变魔术一样，该算法产生了不可知的东西。相关算法已成为我们新兴分析时代的关键组成部分，因为它们解决了将长老会牧师托马斯·贝叶斯 (Thomas Bayes) 18 世纪的统计思想应用于现实世界问题（从有针对性的网络广告到无人驾驶汽车）的关键问题。

We will conclude our exploration of complexity by following an arc that begins with our desire to understand atomic interactions at the start of the atomic and information ages and ends with a new fundamental theorem about complex adaptive systems. In the early 1950s Nicholas Metropolis and others developed an algorithm to explore interacting molecular systems. At the core of this algorithm is a set of simple manipulations that ultimately allows one to recover a critical piece of information that is impossible to generate directly; as if by magic, this algorithm produces the unknowable. Related algorithms have become a critical component in our emerging analytic age, as they solve a key problem in applying the eighteenth-­century statistical ideas of Presbyterian minister Thomas Bayes to real-world problems ranging from targeted web advertisements to driverless cars.

复杂自适应系统的核心是代理寻找更好的结果。通过一些简化，这种搜索行为的关键方面可以与上述算法的元素联系起来。因此，此类系统中的代理在不知不觉中表演了一场由宇宙算法控制的舞蹈。鉴于这种联系，我们推导出复杂自适应系统的新定理，该定理包含了算法固有的魔力。这个新定理意味着，当代理适应这些复杂系统时，它们的适应性受与其潜在适应性相关的概率控制。虽然代理更有可能专注于更好的解决方案，但他们总是有（较低）的机会发现自己处于次优情况。这是一个既令人欣慰又令人谦卑的结果，因为它表明，虽然代理通常会找到最好的结果，但它们有时不可避免地会失败。

At the heart of complex adaptive systems are agents searching for better outcomes. With a few simplifications, the key aspects of this search behavior can be linked to elements of the algorithm above. Thus, agents in such systems are, unknowingly, performing a dance governed by a cosmic algorithm. Given this connection, we derive a new theorem of complex adaptive systems that embraces the magic inherent in the algorithm. This new theorem implies that as agents adapt in these complex systems, their adaptations are governed by probabilities tied to their underlying fitness. While agents are more likely to be found concentrating on the better solutions, there is always a (lower) chance that they will find themselves in suboptimal circumstances. This is a result that is at once both gratifying and humbling, as it suggests that while agents will often find the best outcomes, they will inevitably fail on occasion.

复杂性无处不在。探索其核心原理将带领我们踏上一段穿越上述科学领域的旅程。这段旅程充满敬畏、灵感和最终的洞察力，这些洞察力对于我们科学地理解周围的世界以及我们在面对最具挑战性的问题时生存的能力至关重要。这是一场关于真实地点的旅程，其中的地图并不总是完美的，但它们具有足够的启发性，可以用于我们天生的渴望和探索这一前沿的需求。

Complexity abounds. Exploring its core principles will take us on a journey across the scientific landscapes outlined above. It is a journey marked by awe, inspiration, and ultimately insights that are critical to our scientific understanding of the world around us and to our ability to survive when confronted by our most challenging problems. It is a journey about true places, where the maps are not always well formed, but they are suggestive enough to be of use given our innate desire and need to explore this frontier.

二

two

从简单的开始：互动

From So Simple a Beginning: Interactions

这种对生命的看法是宏伟的，它认为生命具有多种力量，最初被注入几种形式或一种形式；而当这个星球按照固定的引力定律循环往复时，从如此简单的开始，无数最美丽、最奇妙的形式已经并正在进化。

There is grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.

—查尔斯·达尔文， 《物种起源》

—Charles Darwin, The Origin of Species

西我们周围有“无数最美丽、最奇妙的形式”，无论是地球上无数物种中的一种，还是纽约证券交易所等人造建筑。达尔文敏锐的洞察力，将宏伟置于他的生命观中，是，通过可变遗传和自然选择的繁殖，我们可以从简单的开始走向非凡的结局。物理学家菲尔·安德森于 1972 年首次提出了相关见解，这是复杂系统的核心。它认为，简单的部分相互作用，可以产生新的、最奇妙的形式。

We are surrounded by “endless forms most beautiful and most wonderful,” whether they are embodied by one of the myriad of species we find on our planet or in artificial structures such as the New York Stock Exchange. Darwin’s keen insight, the one that put grandeur in his view of life, was that reproduction with variable inheritance and natural selection could move us from simple beginnings to extraordinary ends. A related insight, first postulated by physicist Phil Anderson in 1972, sits at the heart of complex systems. It holds that simple pieces, interacting together, can result in the emergence of new, most wonderful forms.

简单碎片的聚合可能产生新的形式，这一假说被称为“多即是多”假说。这一假说是对现代科学基础的直接挑战。

The potential emergence of new forms from the aggregation of simple pieces is known as the “more is different” hypothesis. This hypothesis is a direct challenge to the foundations of modern science.

现代科学的核心是相信还原论的力量：即我们只需了解世界的各个部分，就能了解世界。因此，如果我们能够完全理解原子，我们就能理解化学，因为化学只是研究原子的集合，从那里我们就能了解生物学，因为它依赖于化学，等等。同样，在社会系统中，如果我们能够理解神经元，我们就能理解大脑，从而了解个人决策，这使我们能够理解群体决策，这使我们能够深入了解政府和企业，最终全面了解整个经济、政治和社会。

At the core of modern science is a belief in the power of reductionism: the idea that to understand the world we only need to understand its pieces. Thus, if we can fully understand atoms, we will then understand chemistry, as chemistry just studies collections of atoms, and from there we will know biology, as it relies on chemistry, and on and on. Similarly, in social systems, if we can understand a neuron, we will understand the brain, and thus know individual decision making, which allows us to understand group decision making, which gives us deep knowledge of governments and firms, and ultimately a full understanding of economics, politics, and society at large.

“多即是多”假说的关键见解是，还原论并不意味着建构论。也就是说，即使我们能够研究和了解世界上最简单的组成部分，这并不意味着我们能够理解一切，因为世界是由这些组成部分构成的。事实上，为了重建世界，我们必须有一个理论，说明组件组合在一起后如何相互作用。有一句古老的苏菲派谚语说，即使你理解数字 1，并且知道 1加1 等于 2，你也不会理解 2，除非你知道“和”是什么意思。

The key insight from the “more is different” hypothesis is that reductionism does not imply constructionism. That is, even if we can study and know the world’s simplest components, that does not imply that we will understand everything just because the world is constructed from these components. Indeed, to reconstruct the world we have to have a theory of how components, once put together, interact. There is an old Sufi adage that even if you understand the number 1 and know that 1 and 1 make 2, you don’t understand 2 until you know what “and” means.

以本页上的字母为例。每个字母由每英寸几百个点组成，这些点彼此之间关系密切。然而，这些点中存在着某种内在的东西，即使点之间的关系有所改变，字母仍能显现出来，正如您可能在某些网页上发现的 CAPTCHA 挑战的扭曲图像中所看到的那样（见图 2.1）。

Take the letters on this page. Each letter is composed of a few hundred dots per inch in careful relation to one another. Yet there is something inherent in these dots that allows letters to emerge, even if the relationship of the dots is somewhat altered, as you might see in the distorted image from a CAPTCHA challenge found on some web pages (see Figure 2.1).

图 2.1：全自动公共图灵测试（CAPTCHA）中扭曲的字母，用于区分计算机和人类，依赖于人类思维中字母形式出现的固有复杂性。

Figure 2.1: The distorted letters of a Completely Automated Public Turing Test to Tell Computers and Humans Apart (CAPTCHA) rely on the complexity inherent in the emergence of letter forms within the human mind.

此外，当字母彼此靠近时，它们会呈现出新的属性和意义，最终导致单词的出现。这种出现非常强烈，即使我们打乱每个单词的开头和结尾之间的字母，它仍会持续存在，也就是说，这种冲突非常强烈，即使我们把每个单词的开头和结尾之间的字母组合起来，它也会持续存在。

Moreover, the letters, when placed near one another, take on new properties and meaning, and ultimately result in the emergence of words. Such emergence is so strong that it persists even if we scramble the letters between each word’s start and end, that is, such eregmnece is so stnorg taht it pesstirs eevn if we sabcmlre the ltteres betewen ecah wrod’s satrt and end.

阐明上述思想的是数学的一个分支，它由才华横溢的约翰·冯·诺依曼发起，研究称为细胞自动机的结构。先从空棋盘开始，然后在最上面一行随机放置一些棋子。对于接下来的每一行，我们将根据上一行中已占用方格的模式和一些固定规则将棋子放置在特定方格中。例如，假设规则是，只有当方格上方的方格被占用时，您才会在该方格上放置棋子。如果我们严格遵循此规则，则每个新行都会复制上一行，慢慢地，我们的棋盘将充满垂直条纹，这些条纹位于我们恰好在最上面一行放置随机棋子的位置。显然，这条规则相当无聊，但它确实暗示了一条简单、非常局部的规则（它只查看上方的方格并忽略较远的方格）如何产生全局模式，在这种情况下，一组垂直条纹，如果您愿意放纵的话，它们类似于斑马的条纹。

Illustrating the above ideas is a branch of mathematics—initiated by the freakishly accomplished John von Neumann—that studies structures called cellular automata. Start with an empty checkerboard, and across the top row randomly place some checkers. For each subsequent row, we will place a checker in a particular square based on the pattern of occupied squares in the row above and some fixed rule. For example, suppose the rule is that you only place a checker on a square if the square immediately above it is occupied. If we dutifully follow this rule, each new row will duplicate the row above, and slowly our checkerboard will be filled with vertical stripes located wherever we happened to have placed a random checker in the top row. Obviously, this rule is rather boring, though it does hint at how a simple, very localized rule (it just looks at the square immediately above and ignores squares that are more distant) can result in a global pattern, in this case a set of vertical stripes that, if you are willing to be indulgent, resemble the stripes of a zebra.

让我们给规则增加一点复杂性。假设我们的规则不仅取决于上方的方格，还取决于该方格左侧和右侧的邻居。这种类型的规则可能有 256 条，并且我们预先考虑一下，使用以下形式之一：如果上方三个方格中只有一个被占用，或者只有上方的方格及其右侧邻居被占用，则添加一个棋盘格，否则将其留空（对于这种类型的爱好者来说，这称为规则 30）。图 2.2 说明了可能从此规则中出现的模式之一。请注意，该模式有一个可爱的主题，即各种大小的倒三角形被放置在看似随机的位置。此外，请注意其中一些结构如何延伸到棋盘的许多方格。如此大规模的结构令人惊讶，因为任何单个方格都只使用其上方三个方格的信息，但形成的结构却跨越数十个方格，而不仅仅是三个方格。

Let’s add a bit of complication to the rule. Suppose our rule depends not only on the square above but also on that square’s immediate left- and right-side neighbors. There are 256 possible rules of this type, and with some malice aforethought, let’s use one of the following form: if only one of the three squares above is occupied or if only the square above and its right-side neighbor are occupied, then add a checker, otherwise leave it empty (for aficionados of this genre, this is known as Rule 30). Figure 2.2 illustrates one of the possible patterns that can emerge from this rule. Notice how the pattern has a lovely theme of inverted triangles of various sizes being placed at seemingly random locations. Furthermore, note how some of these structures extend across many squares of the checkerboard. Such large-scale structures are surprising, given that any individual square uses information only from the three squares immediately above it, yet the structures that form span tens of squares rather than just triplets.

图 2.2：使用规则 30 和随机初始条件从细胞自动机中出现的图案。这里有大量细胞横跨晶格，左侧环绕到右侧，形成一个圆柱体。（由 WolframAlpha 生成。）

Figure 2.2: A pattern emerging from a cellular automaton using Rule 30 and random initial conditions. Here there are a large number of cells across the lattice and the left side wraps around to the right side, forming a cylinder. (Generated by WolframAlpha.)

我们上面的探索证明了这样一个概念：有趣的（甚至可能是复杂的）全球模式可以从简单的局部规则中产生。当然，知道某事是可能的并不意味着它在自然界中存在，即使它存在，也不意味着它很重要。然而，在这种情况下，这种行为似乎是我们世界的重要组成部分。

Our exploration above provides a proof of the concept that interesting (and perhaps even complex) global patterns can emerge from simple local rules. Of course, knowing that something is possible doesn’t mean that it exists in nature or, even if it does, that it is important. However, in this case, such behavior appears to be an important part of our world.

以锥形蜗牛为例，它是一种看似低等的海蜗牛。锥形蜗牛至少有两个令人惊讶之处，使它如此引人注目。首先，它们可能致命，因为它们有鱼叉状的牙齿（从尖端伸出的速度和灵活性令人吃惊），牙齿上附着有毒腺，毒腺中含有一些非常有效的神经毒素。（小心蜗牛！）第二个令人惊讶的现象与本次讨论有关，即某些物种的壳外部有美丽的图案，如图 2.3 所示。

Consider a cone snail, a seemingly lowly species of sea snail. There are at least two surprises that make cone snails remarkable. The first is that they are potentially deadly, as they have a harpoon-like tooth (which comes out of the pointy end with surprising speed and dexterity) that is attached to a poison gland that contains some very effective neurotoxins. (Beware the escargot!) The second surprise, relevant to this discussion, is that the outside of the shell of some species is beautifully patterned, as seen in Figure 2.3.

图 2.3：芋螺（Conus omaria）海螺的壳纹。 （图片由作者拍摄。）

Figure 2.3: The shell pattern on a Conus omaria sea snail. (Photograph by the author.)

这些锥形蜗牛壳图案之所以特别引人注目，是因为它们与上面讨论的细胞自动机中出现的图案相似。我们并不是说锥形蜗牛使用规则 30 来设计它们的外部图案，而只是说，我们所看到的东西可能是由某种局部规则而不是某种全局计划决定的。

What makes these cone snail shell patterns particularly intriguing is their similarity to the patterns that emerge in the cellular automaton discussed above. We are not claiming that cone snails use Rule 30 to pattern their outside, but only that it is possible that some local rule, rather than some global plan, is responsible for what we see.

确实，还有没有其他方法？在一个极端，我们可以想出一个关于贝壳图案的总体规划。随着贝壳的生长，蜗牛根据编码的总体规划知道什么应该放在哪里，并据此指导建造。甚至可以调用智能设计师由此产生的图案，也许是为了给贝壳一些狩猎时的伪装。唉，这样的解释似乎有些多余，因为还有更简单的选择。

Indeed, could it be any other way? At one extreme we could think of a global plan for the pattern of the shell. As the shell grows, the snail knows what goes where based on the encoded master plan and directs the construction accordingly. One could even invoke an intelligent designer for the resulting pattern, perhaps to give the shell some camouflage for hunting. Alas, such explanations seem rather superfluous given a much simpler alternative.

蜗牛的壳通过在其边缘增生而生长。随着新物质的增加，色素沉着由各种化学激活和抑制过程决定，这些过程在物理上必然与局部条件有关。因此，类似“如果附近只有一个深色色素细胞，则增生一个深色色素细胞，否则增生一个浅色细胞”这样的自然规则几乎让我们触及规则 30（可能是因为太多深色细胞会抑制新细胞的形成，而太多浅色细胞会激活深色细胞的形成）。当然，规则 30 也区分了右侧和左侧邻居。然而，这种不对称（称为手性）也出现在生物系统中。例如，在贝壳中，任何特定物种的几乎所有个体都有朝同一方向卷曲的壳。

The snail’s shell grows by accretion at its edge. As it adds new material, the pigmentation is determined by various chemical processes of activation and inhibition that by physical necessity are tied to local conditions. Thus, a natural rule along the lines of something like “If there is only one dark-pigmented cell in your neighborhood, accrete a dark-pigmented cell, otherwise accrete a light-­colored cell” (perhaps because too many dark cells inhibit the formation of new ones and too many light ones activate the formation of a dark one) gets us almost to Rule 30. Of course, Rule 30 also differentiates between right- and left-side neighbors. However, such asymmetry (known as chirality) arises in biological systems as well. For example, in seashells, almost all individuals in any given species have shells that coil in the same direction.

鉴于上述两种关于锥形蜗牛壳外部图案形成方式的选择——蜗牛维持的总体着色计划，对壳的附加部分进行仔细监控和指导，或者非常局部的化学相互作用决定了附加细胞的着色——不难支持更简单的解释。这种假设唯一不直观的部分是，出现的图案与倒三角主题相似，似乎有点太巧妙了，不可能通过这种局部方式产生。如果不是因为存在如果没有上述细胞自动机提供的证明，我们可能不会相信这样的事情是可能的。

Given the above two options about how the pattern arises on the outside of a cone snail shell—a master pigmentation plan that is maintained by the snail with additions to the shell being carefully monitored and directed, or one where very localized chemical interactions determine the pigmentation of added cells—it is not hard to favor the simpler explanation. The only non-intuitive part of such a hypothesis is that the patterns that emerge, with their riffs on the inverted-triangle theme, seem a bit too clever to be generated by such local means. If not for the existence proof provided by the cellular automata above, we might not believe that such a thing was possible.

局部相互作用可以产生有趣的整体模式，这一观点对进化论有着重要意义。事实上，进化科学的一个新分支，专注于进化与生物发育过程之间的关系，简称为进化发育科学，它接受了这一观点。

The notion that local interactions can result in interesting global patterns has some important implications for evolution. Indeed, a new branch of evolutionary science that focuses on the relationship between evolution and the developmental processes of organisms, called evo-devo for short, embraces this perspective.

考虑一下我们在芋螺壳上看到的图案的用途。在一个由进化驱动的世界里，这种图案更有可能与更成功的芋螺有关，要么是因为它提供了一些直接的适应优势，要么是因为它搭了便车。在这种情况下，这种图案很可能通过为它提供一些伪装或使其对猎物具有吸引力，帮助我们行动缓慢但食肉的海螺。

Consider the purpose of the pattern that we see on the cone snail shell. In a world driven by evolution, that pattern is more likely associated with the more successful cone snails, either because it provides some direct fitness advantage or because it takes a free ride on something that does. In this case, the pattern likely helps our slow-­moving yet carnivorous sea snail either by providing it some camouflage from, or by making it attractive to, its prey.

在上面的棋盘自动机中，我们看到了一个简单的规则如何生成一个全局模式。事实上，对于只依赖于上方方格及其直接相邻方格的自动机，我们只需要 8 位信息就可以定义一个规则。（三个相邻方格有 8 种可能的配置，在每种配置下，我们需要 1 位信息来确定是否在下方方格中放置棋子。）通过对这 8 位中的一位进行微小更改，我们将获得一条新规则，该规则很可能生成一个全新的模式。例如，在图 2.4 中，我们采用了规则 30 并进行了微小更改，即只有当上方三个邻居中恰好有一个棋子时，才放置一个棋子（回想一下，规则 30 就是这样做的，但如果父级和右侧邻居都被占用，它也会放置一个棋子）。

In the checkerboard automata above, we saw how a simple rule can generate a global pattern. Indeed, for automata that only depend on the square above and its immediate neighbors, we need just eight bits of information to define a rule. (There are eight possible configurations of three contiguous squares, and we need one bit of information to determine whether we place a checker in the lower square given each configuration.) By making a minor change to one of these eight bits, we will get a new rule that most likely generates an entirely new pattern. For example, in Figure 2.4 we took Rule 30 and made a minor change, namely, placing a checker only if there is exactly one checker in the three neighbors above (recall that Rule 30 did this, but it also placed a checker if the parent and right-side neighbor were both occupied).

图 2.4：使用规则 22、规则 30 的“单突变”邻居和随机初始条件，从元胞自动机中出现的模式。（由 WolframAlpha 生成。）

Figure 2.4: A pattern emerging from a cellular automaton using Rule 22, a “one-mutant” neighbor of Rule 30, and random initial conditions. ­(Generated by WolframAlpha.)

这条新规则被称为第 22 条规则。如您所见，它会产生更规则、更对称的图案，如果您想伪装自己，这可能不太好。另一方面，这种新图案看起来更大胆，额外的对称性会引发观察者的一些好奇心（至少对于这个观察者而言）。因此，通过对底层化学（规则）的轻微改变，发育过程会产生一种非常不同的图案，这可能会使锥形蜗牛受益——尤其是如果以被额外对称性吸引的好奇人类为食被证明是一种优势的话。无论这个特定的例子如何，核心思想都是，即使是对局部过程的微小改变可以产生重大影响，这一点很重要：从如此简单的开始，无穷无尽的形式……

This new rule is known as Rule 22. As you can see, it results in a more regular and symmetric pattern, which is probably bad if you want to camouflage yourself. On the other hand, this new pattern seems much bolder, and the additional symmetry induces some curiosity in the viewer (at least in this viewer). Thus, by a slight alteration to the underlying chemistry (rule), the development process results in a very different pattern that potentially could benefit the cone snail—especially if feeding on curious humans drawn by the additional symmetry proves to be an advantage. Regardless of this particular example, the core idea, that even small changes to local processes can have big implications, is important: from so simple a beginning endless forms . . .

和任何好的模型一样，细胞自动机能够以非常精确和稀疏的方式捕捉重要现象的本质。通过这样做，它们提供了建设性的证据，证明了简单的局部规则如何产生复杂的全球影响。还有一种同样令人感兴趣的复杂性形式，即复杂的局部行为导致简单的全球结果的系统。这种系统最早在两百多年前被正式讨论，它们构成了我们现代经济的基础。

Like any good model, cellular automata are able to capture the essence of an important phenomenon in a very exact and sparse way. By doing so, they provide a constructive proof of how simple local rules can have complex global implications. There is an alternative form of complexity that is also of interest, namely, systems where complex local behavior results in a simple global outcome. Such systems were first formally discussed more than two hundred years ago, and they form the basis of our modern economy.

1776 年，亚当·斯密出版了《国富论》。他在书中的一段简短文字中写道：“他只想要自己的利益，在这一点上，就像在许多其他情况下一样，他被一只看不见的手牵着，去实现一个他本意没有实现的目标。”近两百年后，1954 年，肯·阿罗和杰拉德·德布鲁为斯密的假设提供了一个正式的存在性证明，即在某些条件下，人们可以找到一组价格，在这些价格下，经济主体——每个人都为了自己的利益——会想要买入或卖出刚好够用的每种商品，以平衡价格，并最大限度地提高社会从贸易中获得的收益。因此，表面上混乱的市场被一个宏伟的时钟所取代，这不是任何人的意图，它使一切都保持平衡，甚至导致了一系列交易，在这些交易中，我们无法在不伤害他人的情况下改善任何人的生活。正如斯密所说：“通过追求他的他往往为了个人利益而促进社会利益，而实际上却比他真正想促进社会利益时更加有效。我从未见过那些假装为公众利益做交易的人做过多少好事。”

In 1776, Adam Smith published An Inquiry into the Nature and Causes of the Wealth of Nations. In a brief passage within this tome he wrote, “He intends only his own gain, and he is in this, as in many other cases, led by an invisible hand to promote an end which was no part of his intention.” Almost two hundred years later, in 1954, Ken Arrow and Gerard Debreu provided a formal existence proof of Smith’s hypothesis, namely, that under certain conditions one can find a set of prices under which economic agents—each out for her own gain—will want to buy or sell just enough of each commodity to equilibrate prices and maximize society’s gains from trade. Thus, the apparent chaos of the marketplace is replaced fortuitously by a grand clockwork, not part of anyone’s intention, that brings everything into balance, and even results in a set of trades whereby we cannot improve anyone’s lot in life without harming someone else. As Smith put it: “By pursuing his own interest he frequently promotes that of the society more effectually than when he really intends to promote it. I have never known much good done by those who affected to trade for the public good.”

史密斯对经济学家所谓的一般均衡的洞察，是数百年来经济思想和智力胜利的非凡弧线的一部分。这种思维往往是为了解决一个悖论。例如，水是生命的基本元素，却很便宜，而钻石是非必需的小玩意，却很昂贵。这怎么可能呢？

Smith’s insights into what economists call general equilibrium are part of a remarkable arc of economic thinking and intellectual triumph spanning hundreds of years. Such thinking is often driven by trying to resolve a paradox. For example, water, an essential element for life, is cheap, while diamonds, an inessential bauble, are expensive. How can this be?

这一难题的答案是，只考虑对某种商品的需求（即所谓的市场需求方）只能让我们了解部分情况。除了考虑对商品的需求，还必须考虑其供应。因此，饮用水是丰富的（尽管这种情况正在发生变化），而钻石却很稀有且（有点）难以找到。中世纪穆斯林经济学家伊本泰米叶在 14 世纪写道：“如果对某种商品的需求增加而其供应量减少，则其价格就会上涨。另一方面，如果商品的供应量增加而对它的需求减少，价格就会下降。” 后来，这种思维得到了约翰·洛克（1691 年）和詹姆斯·丹汉姆-斯图尔特（James Denham-Steuart，他在 1767 年出版的一本书中首次使用了“供给与需求”一词，这比斯密的《国富论》早了九年）等思想家的进一步完善。

The answer to such a conundrum is that considering only the need for a good—the so-called demand side of the market—gives us only part of the picture. Along with the demand for a good, one must also consider its supply. Thus, drinkable water is abundant (though this is changing), while diamonds are rare and (somewhat) difficult to find. The medieval Muslim economist Ibn Taymiyyah wrote in the 1300s, “If desire for the good increases while its availability decreases, its price rises. On the other hand, if availability of the good increases and the desire for it decreases, the price comes down.” Such thinking gets refined in subsequent generations by thinkers such as John Locke in 1691 and James Denham-Steuart (who first used the phrase “supply and demand” in a book published in 1767, just nine years before Smith’s Wealth of Nations).

1870 年，弗莱明·詹金斯发表了一篇论文，《论供给与需求的图形表示及其他在《劳动应用》一书中展示了供需图的威力，在 1890 年阿尔弗雷德·马歇尔 (Alfred Marshall) 对其进行了一些改进和推广之后，每一位崭露头角的经济学家都会在入门课上学习这种图。供需图是一种罕见而非凡的科学图解，它以简单而有价值的方式概括复杂的现实。（其他此类图解包括日常天气图中显示的高压和低压锋等常见图解，以及用于追踪量子场论中特定粒子类别贡献的费曼图等奇特图解。）

In 1870, Fleeming Jenkin published a paper, “On the Graphical Representation of Supply and Demand and Their Application to Labour,” that illustrated the power of the supply and demand graphs that—after some refinements and popularization by Alfred Marshall in 1890—every budding economist learns in her introductory class. The supply and demand diagram is one of those rare and remarkable scientific illustrations that takes a complex reality and summarizes it in a simple, valuable way. (Other such diagrams range from the commonplace, such as the high- and low-pressure fronts shown in the daily weather map, to the exotic, such as Feynman diagrams, used to track the contributions of particular particle classes in quantum field theory.)

供给与需求背后的基本思想很简单（至少事后看来如此）。首先，我们分别考虑商品的潜在供应者和需求者对各种价格变化的反应行为。例如，假设有两个供应商可以以 10 美元的成本生产一种商品，还有两个供应商可以以 30 美元的价格生产这种商品。我们可以绘制一条供应曲线来总结这四个供应商的行为，该曲线显示了在不同价格（y 轴）下将有多少商品可供出售（x轴），如图 2.5 所示。（遗憾的是，此处使用的坐标轴名称是历史遗留的，与通常的科学惯例（在x轴上列出独立变量，这里是价格）不一致。）因此，在 5 美元的价格下，没有人愿意出售，而在 25 美元的价格下，成本为 10 美元的两个供应商都会向市场提供他们的商品，而成本为 30 美元的两个供应商将弃权，依此类推。同样，我们可以通过绘制需求者的潜在行为来总结市场的需求方。假设我们有三个需求者愿意为一件商品支付高达 20 美元，还有一个需求者愿意支付 40 美元。那么，当价格为 30 美元时，只有价值 40 美元的商品需求者会想要购买，而当价格为 20 美元或以下时，所有四个需求者都会想要购买商品。

The basic ideas behind supply and demand are straightforward (at least in hindsight). First, we separately consider the behavior of the potential suppliers and demanders of the good in response to various price changes. For example, suppose we have two suppliers who can produce a good at a cost of $10 and two who can do it for $30. We can summarize the behavior of these four suppliers by drawing a supply curve that shows how many goods will be offered for sale (on the x-axis) under various prices (on the y-axis), as shown in Figure 2.5. (Alas, the axis designations used here are a historical artifact at odds with the usual scientific convention of listing the independent variable—here, the price—on the x-axis.) Thus, at a price of $5, no one is willing to sell, while at a price of $25, both of the suppliers with costs of $10 will offer their goods to the market, while the two suppliers with costs of $30 will abstain, and so on. Similarly, we can summarize the demand side of the market by graphing the potential actions of the demanders. Suppose we have three demanders who would be willing to pay up to $20 for a good, and one that is willing to pay $40. Then, at a price of $30, only the demander with the $40 value for the good will want to buy, while at a price of $20 or below, all four demanders will want to purchase a good.

图 2.5：简单市场中的供需。这个市场有两个卖家，生产成本为 10 美元，两个卖家，生产成本为 30 美元，一个需求者，产品价值为 40 美元，三个需求者，产品价值为 20 美元。在竞争均衡中，我们预计两种商品的交易价格为 20 美元。这些交易将在两个卖家之间进行，卖家的生产成本为 10 美元，一个需求者，产品价值为 40 美元，三个需求者之一，产品价值为 20 美元。

Figure 2.5: Supply and demand in a simple market. This market has two sellers with production costs of $10 and two with costs of $30, and one demander with a value of $40 and three with values of $20. In competitive equilibrium we would expect two goods to be traded at a price of $20. These trades would be among the two sellers with production costs of $10 trading with the one demander with a value of $40 and one of the three demanders with values of $20.

供需图是对大量信息的精妙总结。每条曲线都巧妙地包含了推动市场发展的内在力量。供给曲线反映了当前的生产技术、工人的积极性、必须转化为最终产品的投入品的可用性等。需求曲线反映了个人对商品的渴望、替代商品的可用性以及其他此类因素。

The supply and demand diagram represents a nifty summary of a remarkable amount of information. Neatly contained within each of the curves are the inherent forces that drive the market. The supply curve captures the current production technology, the motivation of workers, the availability of the input goods that must be transformed into the final product, and so on. The demand curve captures the desires that individuals have for the good, the availability of alternative goods, and other such factors.

仅仅了解供给和需求曲线的形状就像知道天气图上的高压和低压区域在哪里一样——有点有趣，但只有当你对两个锋面相互作用时会发生什么有某种理论时才有用。

Knowing the shape of the supply and demand curves alone is like knowing where the high- and low-pressure areas are on a weather map—somewhat interesting, but useful only if you have some theory for what happens when the two fronts interact.

经济学家通常依赖系统会寻求均衡的概念，并根据这一原则预测将会发生什么。当然，我们的世界本身并没有什么表明系统会达到均衡，但这样的假设确实有一些优势。首先，可能存在外力确实倾向于将系统推向静止状态的系统。例如，考虑将一个球扔进碗里——重力会使球滚下山坡，最终会停在碗的最低点（或者，如果碗严重凹陷，则停在其中一个凹痕的底部）。此外，如果你轻轻推一下球，这些力就会合力将它移回原来的位置。当然，并非所有的均衡都如此稳定。例如，如果我们把碗倒过来，小心地把球放在上面保持平衡，球会留在那里，但即使是轻微的空气飘过也会让球离开碗，落到很远的地方。寻找平衡的第二个好处是它往往使分析变得容易得多（尽管有时平衡一旦找到就很容易识别，但一开始就很难找到，比如保险箱的组合）。最后，强调平衡本身就是一种安慰，因为把一个系统看作一个宏伟的钟表的一部分，将世界调整到一个精细的平衡状态，而不是把它看作一个随机游荡的东西，要好得多。

Economists typically rely on the notion that systems will seek out an equilibrium, and from this principle, they predict what will happen. Of course, there is nothing inherent in our world that suggests systems equilibrate, but such an assumption does have a few advantages. First, there may be systems where external forces do indeed tend to push the system to a state of rest. For example, consider dropping a ball into a bowl—the gravitational force will cause the ball to roll downhill, and it will eventually come to rest at the lowest point of the bowl (or, if the bowl is badly dented, at the bottom of one of the dents). Moreover, if you give the ball a slight push from its resting place, the forces will conspire to move it back to its original position. Of course, not all equilibria are so stable. For example, if we invert the bowl and carefully balance the ball on top, the ball will remain there, but even a slight whiff of air will have the ball heading off the bowl and settling somewhere far away. The second advantage of seeking out an equilibrium is that it tends to make the analysis much easier (though sometimes an equilibrium is easy to recognize once you find it but hard to find in the first place, as in the case of a combination on a safe). Finally, an emphasis on equilibrium is innately comforting, as it is much nicer to think of a system as part of a grand clockwork aligning the world into a finely balanced state, rather than as something undergoing random wanderings.

在市场中，经济学家有一个竞争均衡的概念。这个想法很简单：市场应该在一个价格上达到平衡，在这个价格上，供应商想要出售的数量刚好等于需求者想要购买的数量。因此，通过向市场公布这样的价格，对商品的需求将刚好等于商品的供应量，每个想要出售的供应商都能找到想要购买的需求者，从而实现平衡。在我们之前的供需图中，竞争均衡发生在 20 美元的价格下。在这个价格下，两个 10 美元的供应商想要出售，而两个 30 美元的供应商不想出售。在同样的价格下，40 美元的需求者想要购买，而其余三个 20 美元的需求者则无所谓，无论他们买不买，都会同样富裕。因此，竞争均衡理论预测，这三个需求者中只有一个会进入市场并购买，从而实现价格为 20 美元且售出两件商品的平衡。

In markets, economists have a notion of competitive equilibrium. The idea is simple: markets should equilibrate at a price where the amount that the suppliers want to sell just equals the amount that the demanders want to buy. Thus, by announcing such a price to the market, the desire for goods will just equal their availability, and every supplier who wants to sell can find a demander who wants to buy, and equilibrium will ensue. In our previous graph of supply and demand, competitive equilibrium occurs at a price of $20. At this price, the two $10 suppliers want to sell, while the two $30 suppliers do not. At the same price, the $40 demander wants to buy, while the remaining three $20 demanders are indifferent, being equally well off whether they buy or not. Thus, the theory of competitive equilibrium predicts that only one of these remaining three demanders will come onto the market and buy, resulting in an equilibrium with a price of $20 and two goods sold.

令人惊讶的是，竞争均衡中还包含着一个更微妙的结果。如果你考虑一下均衡市场中交易者所获得的总利润，你会发现他们获得了 40 美元（高价值需求者为她估价为 40 美元的东西支付了 20 美元，因此她赚了 20 美元，而两个供应商通过以 20 美元的均衡价格进行交易，各自赚了 10 美元）。有没有办法重新安排交易，以增加总收入？假设高价值需求者与其中一个卖家进行交易，成本为 30 美元，两人共获得 10 美元的利润（利润份额取决于他们商定的具体价格）。这将使两个 10 美元的供应商与剩下的三个 20 美元的需求者打交道，因此会产生两笔额外的交易，每笔交易产生 10 美元的利润。在这里，三笔交易的总利润为 30 美元，比我们之前的利润少 10 美元。事实上，我们可以证明，除了竞争均衡产生的交易模式之外的其他交易模式只会减少所有交易者获得的总利润。

There is, surprisingly, a more subtle result embedded in competitive equilibrium. If you think about the total amount of profit earned by the traders in the equilibrated market, you will see that they walk away with $40 (the high-valued demander paid $20 for something she valued at $40, so she earns $20, and the two suppliers each earn $10 by trading at the equilibrium price of $20). Is there some way to rearrange trades that would increase the total amount earned? Suppose that the high-valued demander traded with one of the sellers with a cost of $30, generating $10 of profit between the two of them (with the share of the profits going to each depending on the specific price they agree upon). This would leave the two $10 suppliers to deal with the three remaining $20 demanders, so two additional trades would result, each generating a profit of $10. Here, the total amount of profit earned by the three trades is $30, which is $10 less than what we had before. Indeed, one can show that trading patterns other than the one resulting from competitive equilibrium will only reduce the amount of total profit earned by all of the traders.

关注最大化贸易总利润非常重要，因为如果我们不最大化这一利润，我们就失去了让至少一个人受益而不损害其他任何人的机会（假设我们的交易者只关心他们的个人利润）。为了理解这一点，假设市场结果在由此产生的交易组合并不能使总利润最大化。在这个低效市场中赚取的总利润以某种方式在交易者之间分配。现在，重新运行市场并最大化总利润。由于最大化的利润大于低效市场的利润，这次我们有足够的利润让每个交易者获得她在低效市场中赚取的利润，并且仍然有一些剩余利润。然后，我们可以把剩余的利润分给一个（或多个）交易者，让接受者受益而不损害任何其他人。后一种见解，加上交易者只为自己着想的想法，让我们回到了史密斯所写的：“在这种情况下，就像在许多其他情况下一样，他被一只看不见的手引导着，去实现一个他本意没有实现的目标。”

The focus on maximizing the total profit from trade is important, since if we are not maximizing this profit, we are losing out on an opportunity to make at least one person better off without harming anyone else (assuming our traders only care about their individual profits). To see this, suppose that the market outcome is inefficient in the sense that the resulting set of trades does not maximize total profit. Whatever total profit was earned in this inefficient market gets divided among the traders somehow. Now, rerun the market and maximize total profits. Since the maximized profits are greater than the profits from the inefficient market, this time we have enough profit to give every trader exactly what she earned in the inefficient market and still have some profit left over. We can then take this leftover profit and give it to one (or more) of the traders, making the recipient(s) better off without harming anyone else. This latter insight, plus the idea that the traders are out for themselves, brings us full circle back to what Smith wrote: “He is in this, as in many other cases, led by an invisible hand to promote an end which was no part of his intention.”

复杂系统视角的市场观与上述观点不同。回想一下，为了平衡市场，我们首先宣布了竞争均衡价格，从此一切顺利。但这个价格从何而来？市场由个体供应商和需求者组成，每个人只知道自己的销售成本或购买价值。鉴于此，竞争均衡价格是如何产生的？正如复杂系统视角的早期支持者弗里德里希·哈耶克在 1945 年明确指出的那样：

The complex-systems view of markets differs from the above account. Recall that to equilibrate the market, we first announced the competitive equilibrium price, and from there, all was well. But where did that price come from? The market is composed of individual suppliers and demanders, each of whom knows only her own cost of selling or value of buying. Given this, how does the competitive equilibrium price ever emerge? As Friedrich Hayek—an early proponent of the complex-systems perspective—made clear in 1945:

因此，如果我们能够证明，所有的事实，如果它们都被一个人所知（我们假设它们被提供给观察者），那么这个问题就无法得到解决。经济学家）将唯一地确定解决方案；相反，我们必须展示解决方案是如何通过每个人只拥有部分知识的人们的互动产生的。假设所有知识都集中在一个人的头脑中，就像我们假设知识被给予我们这些解释经济学家一样，就是假设问题不存在，忽视了现实世界中所有重要和有意义的事物。

The problem is thus in no way solved if we can show that all the facts, if they were known to a single mind (as we hypothetically assume them to be given to the observing economist), would uniquely determine the solution; instead we must show how a solution is produced by the interactions of people each of whom possesses only partial knowledge. To assume all the knowledge to be given to a single mind in the same manner in which we assume it to be given to us as the explaining economists is to assume the problem away and to disregard everything that is important and significant in the real world.

回答哈耶克的挑战可能并不像乍看起来那么无望，因为我们可以假设某种市场机制——例如，一位拍卖师站在所有人面前宣布潜在价格，了解有多少供应商和需求者想以每个价格进行交易，通过这种繁琐的工作，她可以得出竞争均衡价格。当然，我们在现实世界中看不到这样的拍卖师。相反，我们看到的是各种拍卖机构，比如纽约证券交易所的专家，或者在芝加哥商品交易大厅里互相喊叫和打手势的穿着色彩鲜艳夹克的交易员。

Answering Hayek’s challenge may not be as hopeless as it appears at first blush, as we may be able to hypothesize some market mechanism—for example, an auctioneer who stands up in front of everyone and announces potential prices, getting a sense of how many suppliers and demanders want to trade at each price, and from this tedious exercise she can generate the competitive equilibrium price. Of course, we see no such auctioneers in the real world. Instead we see various auction institutions such as specialists in the New York Stock Exchange or the colorfully jacketed traders yelling and gesturing to one another in the commodity pits of Chicago.

不幸的是，要得出一个关于市场价格如何产生的有理有据的理论极其困难。虽然竞争均衡理论天生就令人信服，因为任何供需不平衡都会推动价格，从而使交易趋于一致，但很难想象这种力量在现实世界中是如何实际引导的。

Unfortunately, it has been extremely difficult to derive a well-grounded theory of how prices arise in markets. While the theory of competitive equilibrium is innately compelling given that any imbalances in supply and demand should push prices in a way that will bring trades in line, it is hard to imagine how such forces are actually directed in the real world.

我们能否自下而上地构建一个替代性的复杂系统市场理论？也就是说，我们能否对交易做出一些简单的假设，并据此展示全球交易和价格模式是如何出现的？

Can we build an alternative complex-systems theory of markets from the bottom up? That is, can we make some simple assumptions about trading and, from these, show how global patterns of trades and prices emerge?

我和我的同事 Michele Tumminello 一直在研究这种方法，我们考虑了一个简单的交易市场。在这个交易市场中，交易者四处游荡，偶遇对方。当他们见面时，交易者会脱口而出一个随机报价，唯一的条件是，如果该报价被接受，交易者将不会亏损。为了使这个概念更简单，我们假设如果两个交易者相遇，并且有可能进行互利交易，他们将以供应商成本和需求者价值的中点给出的价格进行交易（这是一个很容易的扩展，可以让交易者更腼腆一点）。如果两个交易者无法就交易达成一致，他们会继续四处游荡，偶遇新的潜在贸易伙伴。

My colleague Michele Tumminello and I have been pursuing this approach by considering a simple trading bazaar. In this bazaar, traders wander around and bump into one another. When they meet, traders blurt out a random offer, with the only proviso being that if that offer is accepted, the trader will not lose money. To make this conceptually simpler, let’s just assume that if two traders bump into each other and there is the possibility of a mutually profitable trade, they will trade at a price given by the midpoint between the supplier’s cost and the demander’s value (it is an easy extension to make the traders a bit more coy). If two traders cannot agree on a deal, they continue to wander around and bump into new potential trading partners.

在这样的集市中，使用上面讨论的同一组供应商和需求者，可能会出现两种交易配置。第一种与竞争均衡下的交易配置密切相关，即 40 美元的需求者与 10 美元的供应商进行交易（价格为 25 美元），而 20 美元的需求者之一与另一个 10 美元的供应商进行交易（价格为 15 美元）。请注意，虽然这些是参与竞争均衡下交易的相同交易者，但价格不同，因为竞争均衡预测两笔交易的价格都是 20 美元，而不是这里预测的 25 美元和 15 美元。

In such a bazaar, using the same set of suppliers and demanders discussed above, there are two possible configurations of trades that can arise. The first, closely related to that arising under competitive equilibrium, has the $40 demander trading with a $10 supplier (at a price of $25) and one of the $20 demanders trading with the other $10 supplier (at a price of $15). Note that while these are the same traders that are involved in transactions under competitive equilibrium, the prices differ, since competitive equilibrium predicts that both trades will occur at a price of $20, versus the $25 and $15 predicted here.

另一种交易配置也是可能的。假设 40 美元的需求者最初遇到 30 美元的供应商之一。在这种情况下，他们将同意以 35 美元的价格进行交易。此时，唯一可以达成双方同意的交易配对是 20 美元的需求者和 10 美元的供应商之间的配对，因此我们预测最终将发生两笔这样的交易（因为我们有三个这样的需求者，但只有两个这样的供应商），价格为 15 美元。因此，如果历史按照这种情况展开，我们会得到三笔交易，一笔价格为 35 美元，两笔价格为 15 美元。这种配置与我们在竞争均衡下预测的配置完全不同，而且它是低效的，因为所有交易者获得的总利润只有 30 美元，而我们在竞争均衡下获得的利润为 40 美元。因此，整个系统损失了 10 美元的额外利润，这笔利润本可以用来改善至少一个人的命运。

An alternative trading configuration is also possible. Suppose instead that the $40 demander initially bumps into one of the $30 suppliers. In this case, they will agree to trade at a price of $35. At this point, the only remaining pairings that can result in mutually agreeable trades are between the $20 demanders and $10 suppliers, so we would predict that two such trades will occur eventually (since we have three such demanders but only two such suppliers) at a price of $15. Thus, if history unfolds as in this scenario, we get three trades, one at a price of $35 and two at a price of $15. This configuration is quite different from what we would predict under competitive equilibrium, and it is inefficient in the sense that the total profit earned across all of the traders is only $30, versus the $40 we get under competitive equilibrium. Thus, the system as a whole lost out on $10 of additional profit that could have been used to improve at least one person’s lot.

虽然这有点繁琐（没有计算机，尤其是对于大型系统），但人们可以计算出上述两种配置在集市中出现的可能性。大约三分之一的时间（准确地说是 8/25），我们将得到与竞争均衡结果相关的配置，而替代配置将在大约三分之二的时间（17/25）出现。

While it is somewhat tedious (without a computer, especially for big systems), one can work out the likelihood of the two configurations above arising in the bazaar. About one-third of the time (8/25, to be exact), we will get the configuration associated with the competitive equilibrium outcome, and the alternative configuration will arise around two-thirds of the time (17/25).

因此，在集市模型下——充分承认其中的文字游戏的可能性——大约有三分之一的机会，我们最终会得到与竞争均衡下相同的交易，尽管可能性略有增加。不同的价格。剩下的三分之二的时间里，我们预计会看到截然不同的结果，一笔交易的价格为 35 美元，两笔交易的价格为 15 美元。在这两个世界中，交易者只为自己的利益行事，产生了一种不属于任何人意图的结果，即一套价格和一种交易模式，导致整个社会产生一定的总利润。

Thus, under the bazaar model—with the potential for easy wordplay fully acknowledged—there is roughly a one-third chance that we will end up with the same trades that we see under competitive equilibrium, though at slightly different prices. The remaining two-thirds of the time we expect to see a very different outcome, with one trade at $35 and two at $15. In both worlds, traders acting only in their own interests produce an outcome that was no part of anyone’s intention, namely, a set of prices and a pattern of trades that result in some aggregate profit across society.

鉴于上述两种模型，我们应该相信哪一种呢？这是一个难题。如果我们查看实验市场（与上述市场类似，但交易者更多）生成的数据（见图 2.6），我们会看到数据中的峰值对应于我们从集市模型预测的中点值，而不是竞争均衡预测的统一价格。当然，对于任何行为模型，我们都允许一定的误差空间。因此，价格不太一致是可以预料的，需要判断不一致的价格是更接近竞争均衡模型的价格还是集市模型的价格。根据我们的数据，似乎不能轻易否定集市模型。

Given the above two models, which one should we believe? This is a difficult question. If we look at data (see Figure 2.6) generated in experimental markets (similar to the one above but with many more traders), we see peaks in the data that correspond to the midpoint values we predict from the bazaar model, rather than the uniform price predicted by competitive equilibrium. Of course, with any model of behavior, we allow some room for error. Thus, having prices that don’t quite line up is expected, and one needs to make a judgment about whether the misaligned prices are closer to those emerging from the competitive equilibrium model or those from the bazaar model. Given our data, it seems that the bazaar model cannot easily be dismissed.

对同一现象的不同看法通常有助于更深入地了解一个系统。在许多方面，竞争均衡和集市模型相互补充，提高了我们对市场的理解。当然，学术范式往往围绕某一特定观点而固化，而改变这一观点的能力则取决于该领域。例如，在物理学中，能更好地解释数据的简单模型往往很快就会胜出。在经济学中，接受可能更好地解释数据的新方法是一个缓慢得多的过程。直到最近，经济学家才开始忽视实验数据，通常采用一种非常规定的建模范式，这种范式依赖于优化和均衡。最终，我们必须遵循肯尼斯·博尔丁的第一定律，即“任何存在的事物都是可能的”——这是一个显而易见且有用的观察结果，但经常被忽视。

Different views of the same phenomenon are often useful in gaining a deeper understanding of a system. In many ways, the competitive equilibrium and bazaar models complement each other, improving our understanding of markets. Of course, academic paradigms often solidify around a particular view, and the ability to alter this point of view depends on the field. In physics, for example, simple models that better explain the data tend to quickly win the day. In economics, accepting new approaches that may better explain the data is a much slower process. Economists ignored experimental data until relatively recently and typically embrace a very prescribed modeling paradigm that relies on optimization and equilibrium. Ultimately, we must follow Kenneth Boulding’s first law, namely, “Anything that exists is possible”—an obvious and useful observation that often gets ignored.

图 2.6：一些以人类为对象的实验市场的价格分布。每个市场都有多个受试者，需求方价值分别为 20 美元和 40 美元，卖方生产成本分别为 10 美元和 30 美元。图中的每一幅图都显示了买方和卖方之间观察到的交易价格分布，其值分别为（s表示卖方成本为 10 美元，S表示卖方成本为 30 美元，b表示买方价值为 20 美元，B表示买方价值为 40 美元）。竞争均衡预测所有交易都将以 20 美元的价格进行（在预测交易的分布中用浅色垂直线表示），并且每笔交易中潜在的买方价值和卖方成本不会对观察到的价格分布产生影响。集市模型预测交易价格为买方价值和卖方成本之间的中间价格（在预测交易的分布中用深色垂直线表示）。

Figure 2.6: Price distributions arising from some experimental markets with human subjects. Each market had multiple subjects, with demander values of $20 and $40, and seller production costs of $10 and $30. Each panel of the figure shows the distribution of observed trading prices between buyers and sellers with the indicated values (s for seller costs of $10, S for seller costs of $30, b for buyer values of $20, and B for buyer values of $40). Competitive equilibrium predicts that all trades will occur at a price of $20 (indicated by the light vertical lines in those distributions where trades are predicted) and that the underlying buyer value and seller cost in each trade will make no difference in the distribution of observed prices. The bazaar model predicts trades at the intermediate price between the buyer values and seller costs (indicated by the dark vertical lines in those distributions where trades are predicted).

竞争均衡或集市模型是否能正确描述我们的世界，这仍是一个悬而未决的问题。图 2.6 所示的实验市场中，交易者天真，显然带有交易集市而非精心策划的市场的特征。事实上，如果我们的交易者发现自己日复一日地身处同一个市场，或者我们引入一些额外的参与规则，人们可能会更加信任竞争均衡模型——例如，也许买入和卖出必须清楚地张贴出来，让所有人都能看到，所有人都能接受。这些额外的条件可能会使市场结果更接近竞争均衡的预测。

Whether the competitive equilibrium or bazaar model is the right description of our world is an open question. Experimental markets with naive traders, like those shown in Figure 2.6, certainly seem to carry the signature of a trading bazaar rather than a carefully orchestrated market. Indeed, one might put more faith in the competitive equilibrium model if our traders found themselves in the same market day after day, or if we introduce some additional rules of engagement—for example, perhaps bids and offers must be clearly posted for all to see and for anyone to accept. Such additional conditions might push the outcome of the market more toward the predictions of competitive equilibrium.

无论如何，这两种模型都很有趣，因为它们包含了复杂系统的基本概念：个体之间的互动可能导致全球结果的出现 - 在这种情况下，价格和交易模式 - 而这并不是任何人的意图。

Regardless, both models are interesting in that they embrace the fundamental notion of complex systems: that interactions among individuals can result in the emergence of global outcomes—in this case, patterns of prices and trades—that were no part of anyone’s intention.

一百多年来，经济学家一直依靠竞争均衡模型来预测市场将如何表现，进而预测应该如何制定政策。竞争均衡模型和供需工具是科学的真正胜利。再考虑一下我们面临的根本问题在分析市场时。潜在的交易者只知道自己的价值和成本，他们聚在一起试图彼此达成自利交易。这些潜在的交易者，有的无聊而疲惫，有的积极而敏锐，他们随机聚在一起，试图达成一笔有利可图的交易，因为他们一路上从同行的叫喊声和低语声中收集信息。也许有些交易者是精于算计的思想家，他们根据所面临的有限信息得出最佳的交易规则，而另一些交易者则更加鲁莽，胡乱交易。

For more than one hundred years, economists have been relying on the competitive equilibrium model to predict how markets will behave and, in turn, how policies should be made. The competitive equilibrium model and the tools of supply and demand are a real triumph of science. Consider again the fundamental problem we face when analyzing a market. Potential traders, knowing only their own values and costs, come together to try to make self-interested deals with one another. These potential traders, some bored and tired, others motivated and sharp, randomly get together and try to close a profitable deal as they gather pieces of information from the shouts and murmurs of their fellow traders along the way. Perhaps some traders are calculating thinkers who derive the best trading rules possible given the limited information they face, while others are more reckless and trade willy-nilly.

混乱中诞生了秩序，以交易和价格流的形式出现。竞争均衡的概念是这种秩序的极端版本​​，嘈杂的叫喊声导致单一价格足以平衡每个人的交易意愿，卖家提供的商品刚好足以满足买家的需求，由此产生的交易使市场总利润最大化。在这样的模型中，即使取代其中一种交易也会导致社会财富减少。

Out of such chaos comes order, in the form of a stream of trades and prices. The idea of competitive equilibrium is an extreme version of such order, where the cacophony of shouts results in a single price sufficient to balance everyone’s desire to trade, with just enough goods being offered by the sellers to meet the buyers’ demands, and the resulting trades maximizing the total profit available in the market. In such a model, displacing even one of these trades would result in society having less.

另一个秩序故事是交易市场。在这个世界里，我们拒绝接受出现独特、全球、竞争均衡价格的想法，我们接受交易者的混乱阴谋。潜在买家随机遇到潜在卖家，并提出看似随机产生的报价。当报价导致互利交易时，它就会被接受，交易者就会离开市场。同样，在市场中出现了一组可预测的价格和交易（尽管这里的确定性稍差一些）。市场。其结果肯定比竞争均衡的结果更加混乱，而且现在才刚刚开始对这两种方法的性能和效用进行正式测试。

An alternative tale of order is that of the trading bazaar. In this world, we dismiss the notion that a unique, global, competitive equilibrium price emerges, and we embrace the chaotic machinations of the traders. Potential buyers randomly encounter potential sellers, and seemingly randomly generated offers are proffered. When an offer results in a mutually profitable trade, it is accepted and the traders leave the market. Again, a predictable (though here with a bit less certainty) set of prices and trades emerges in the market. The result is certainly messier than that arising in competitive equilibrium, and formal tests of the performance and utility of the two approaches are only now being conducted.

局部相互作用形成意想不到的全球模式的力量是惊人的。无论这些局部相互作用是导致海螺壳上美丽的图案，还是导致最大化社会财富的一套价格和交易，从这些简单的开端，奇妙的形式正在涌现。

The power of local interactions to form unexpected global patterns is remarkable. Whether these local interactions lead to the beautiful design on the shell of a sea snail or to a set of prices and trades that maximize society’s bounty, from such simple beginnings wonderful forms are emerging.

三

three

从闪电崩盘到经济崩溃：反馈

From Flash Crashes to Economic Meltdowns: Feedback

尽管我们并不认为整个国家的问题是一个泡沫，但很明显这是一种不可持续的潜在模式。

Without calling the overall national issue a bubble, it’s pretty clear that it’s an unsustainable underlying pattern.

—艾伦·格林斯潘

—Alan Greenspan

哦2010 年 5 月 6 日星期四，美国东部标准时间下午 2:32，一系列事件开始发生，导致证券市场在接下来的半小时内陷入混乱。在这一时期的最初几分钟内，美国主要股指暴跌 5% 至 6%（见图 3.1）。下午 2:45，市场暂停交易五秒钟，股指奇迹般地反弹。然而，股指引发的海啸开始席卷整个股市。三百多只股票的交易价格与之前的价值相比偏离了 60% 以上。随着一些股票的流动性枯竭，市场崩溃，在极端情况下，曾经备受推崇的公司的股价开始大幅波动，埃森哲等公司的股价从之前的 40 美元跌至仅售 1 美分，而苹果公司的股价则迅速从 250 美元涨至 100,000 美元。到下午 3 点，海啸逐渐平息，市场恢复正常。

On Thursday, May 6, 2010, at 2:32 p.m. Eastern Standard Time, a sequence of events began that led to chaos in the securities markets for the next half an hour. During the first few minutes of this period, major United States equity indices plummeted 5–6 percent (see Figure 3.1). At 2:45 p.m. a five-second trading pause was imposed on the market, and the indices miraculously rebounded. However, the tsunami that started in the indices began to wash over the entire equities market. Trading prices for more than three hundred individual stocks deviated by more than 60 percent of their previous values. As liquidity dried up in some stocks, markets failed, and at the extreme the prices of shares in formerly well-regarded companies began to fluctuate wildly, with a company such as Accenture, previously trading at $40, selling for only a penny, and shares of Apple quickly moving from $250 to $100,000. By 3:00 p.m. the tsunami had subsided, and the markets returned to more normal behavior.

图 3.1： 2010 年 5 月 6 日美国主要市场指数，包括道琼斯工业平均指数 (DJIA，左侧刻度) 和标准普尔 500 指数 (S&P 500 Index，右侧刻度)。（来源：美国证券交易委员会。）

Figure 3.1: Major US market indices on May 6, 2010, including the Dow Jones Industrial Average (DJIA, left-hand scale) and the Standard and Poor’s 500 Index (S&P 500 Index, right-hand scale). (Source: US Securities and Exchange Commission.)

什么可能引发如此动荡？是新闻报道了一场灾难性事件，比如一场大战爆发或一位重要世界领导人遇刺？是某个欧洲国家突然拖欠债务？是恐怖分子袭击美国本土或对交易系统发动网络攻击？唉，触发事件比上述任何事件都更平凡，也更令人担忧。

What could have possibly started such turmoil? Was there some news report of a cataclysmic event, like a major war breaking out or the assassination of a key world leader? Did some European country suddenly default on its debt? Was there some terrorist strike on the homeland or cyberattack on the trading system? Alas, the triggering event was at once far more mundane, and far more worrisome, than any of these.

上述混乱的直接原因似乎是由一家资金管理公司发起的一系列交易，该公司的地址是堪萨斯州肖尼传教团的一个邮政信箱。该公司使用计算机交易程序出售一些证券，依靠一种算法将其交易行为仅与市场上的当前交易量挂钩，而不是与证券价格等更明显的因素挂钩。虽然事后看来，很容易看出这样的程序如何引发市场波动，但更大的担忧是，复杂金融系统中不断增长的相互联系和相互作用如何足以让这种波动发展成一场全面的海啸，至少在半小时内，对金融海岸造成了严重破坏。

The proximate cause of the above turmoil appears to have been a set of trades initiated by a money-managing firm whose address was a post office box in Shawnee Mission, Kansas. This firm used a computerized trading program to sell some securities, relying on an algorithm that tied its trading behavior only to the current volume of trades on the market, rather than to a more obvious factor such as the security’s price. While in hindsight it is easy to see how such a program could induce a ripple in the market waters, the far greater concern is how the ever-growing set of interconnections and interactions across the complex financial system was sufficient to allow this ripple to grow into a full-fledged tsunami that, at least for half an hour, wreaked havoc upon the financial shores.

2010 年 9 月，美国商品期货交易委员会和美国证券交易委员会就恰如其名的“闪电崩盘”发布了一份联合报告，题为《2010 年 5 月 6 日市场事件调查结果》 ，下文的许多市场细节均来自该报告。该报告对当天发生的事件进行了详细的经济剖析，总的来说，对于那些倾向于探索细节的人来说，这是一本相当不错的读物（而且很容易下载）。就像任何好的剖析一样，包含在其枯燥的描述和细致的分析，构成了关于死亡原因的精彩故事。然而，真正的吸引力来自于未讨论的内容，即关于谁干了这事、为什么干了这事以及这事是否可以避免的谜团。

In September 2010, the US Commodity Futures Trading Commission and the US Securities and Exchange Commission released a joint report on the aptly named “flash crash,” entitled Findings Regarding the Market Events of May 6, 2010, and many of the market details below are drawn from this source. The report provides a detailed economic autopsy of the events that unfolded on that day, and it’s rather good reading (and easily available by download), all things considered, for those inclined to explore the intimate details. Like any good autopsy, contained within its dry descriptions and careful analyses is a remarkable story of how the death came about. Yet the real intrigue comes from what is not discussed, namely, the mystery about who did it, why, and whether it could have been avoided.

2010 年 5 月 6 日，金融市场已经处于紧张状态。欧洲债务危机主导着政治和经济格局，尤其是希腊可能拖欠债务的可能性。各种市场指标的变化，如预期的股市波动、债务保险溢价、欧元汇率以及黄金和美国国债等安全证券的价格，都反映了这些情况带来的不安。这些变化可能将市场推向一个关键状态（我们将在第 11 章中探讨这一观点），即使是一个小事件也有可能引发更大的连锁反应。

May 6, 2010, had begun with the financial markets already on edge. The European debt crisis dominated the political and economic landscape, especially the possibility that Greece might default on its debts. Changes in various market indicators, such as the expected stock market volatility, the premium on debt insurance, the exchange rate of the euro, and the prices of gold and safe securities such as Treasuries, all reflected the unease brought about by these conditions. These changes likely pushed the markets toward a critical state (an idea that we will explore in Chapter 11), where even a small event had the potential to cascade into a much larger chain reaction.

海啸的开始很无辜。一家管理共同基金的公司希望对冲其现有的股票头寸，以防美国股市未来变化。这是一种普遍的愿望，因为该公司可能希望锁定最近获得的一些利润，以防美国股市下跌。为了实现这一对冲，该公司希望出售 75,000 份将于 6 月到期的 E-mini 期货合约。E-mini 是一种衍生证券，也就是说，它们的价值与其他东西挂钩——在这种情况下，每份 E-mini 的价值是标准普尔 500 指数价值的 50 倍（约占市值的 70%）占所有美国上市股票的 100% 以上）。因此，如果标准普尔 500 指数为 1,000 美元，那么每份 E-mini 的价值就是该指数的 50 倍，即 50,000 美元。75,000 份合约约占 2010 年日均交易量的 3.4%，按现行价格计算，总价值约为 41 亿美元。单个个人想要出售 75,000 份合约的情况并不常见，尽管在过去 12 个月中曾有两次交易规模达到或超过这一水平。

The start of the tsunami began innocently enough. A firm that managed mutual funds wanted to hedge its existing equity positions against future changes in the US equities market. This is a common desire, as presumably the firm wanted to lock in some profits it had recently gained against the possibility that the US equities market might decline. To accomplish this hedge, the firm wanted to sell 75,000 E-mini futures contracts that would become due that June. E-minis are a derivative security, that is, their value is tied to something else—in this case, each one is worth fifty times the value of the S&P 500 Index (which represents about 70 percent of the market capitalization of all US-listed equities). Thus, if the S&P 500 Index is at $1,000, each E-mini is worth fifty times that, or $50,000. The 75,000 contracts represented roughly 3.4 percent of the average daily volume traded during 2010, and they were worth a total of about $4.1 billion at the prevailing price. Having a single individual wanting to sell 75,000 contracts is unusual, although there had been two occasions in the preceding twelve months where trades of this size or larger had been conducted.

此类交易并非没有风险。一次性出售如此大量股票的问题在于，如果不小心，很容易导致价格暴跌。假设您决定一次性将大量股票全部抛售到市场上。最初，如果市场流动性强，会有一些买家以大致相同的价格购买您的股票。当这些买家的需求得到满足时，他们就会离开市场，您的股票开始流向交易所在其“订单簿”中记录的预先存在的购买要约。当您的股票满足这些预先存在的最高报价时，它们接下来会流向较低的报价，如此反复。随着您的订单大量进入订单簿，价格继续下跌，任何进入市场的潜在新买家都会意识到正在发生的事情，并预计价格会下降，从而对价格造成更大的下行压力。尽管任何大规模的出售要约都会倾向于压低整体价格，但考虑到订单簿的微观动态，一次性将股票全部抛售到市场上一次出售将产生较大的、短暂的影响，导致卖方获得的整体价格比股票出售速度较慢时所能获得的价格要差得多。

Such trades are not without hazards. The problem with selling such a large number of shares all at once is that you can easily cause the price to plummet if you are not careful. Suppose you decide to sell a large number of shares by just dumping them all on the market at once. Initially, if the market is liquid, there are some buyers around to purchase your shares at roughly the going price. As these buyers’ demands are satisfied they leave the market, and your shares begin to flow to preexisting offers to buy that have been recorded by the exchange in its “order book.” As your shares satisfy the highest of these preexisting offers, they next flow to lower ones, and on and on. As your orders eat well into the order book, prices continue to fall, and any potential new buyers coming onto the market recognize what is happening and make much less aggressive offers in anticipation of lower prices, putting even more downward pressure on prices. While any large offer to sell will have a tendency to depress the overall price regardless, given the microdynamics of the order book, dumping the shares on the market all at once will have a larger, short-lived impact, resulting in the seller getting much worse prices overall than she could have gotten if the shares were sold more slowly.

因此，为了获得大宗订单的最佳价格，卖方需要谨慎管理交易区块并缓慢地将股票投放到市场上。这样一来，新买家就可以在销售过程中找到进入市场的途径，在此过程中重新填满订单簿，最终使卖方获得整个批次的更高价格。

Thus, to get the best prices possible for a large order, the seller needs to carefully manage the block of trades and slowly release shares onto the market. This allows new buyers to find their way to the market during the sale, refilling the order book in the process, and ultimately resulting in the seller getting much higher prices overall for the entire lot.

管理大宗交易的一种方法是采用自动交易算法，以合理的方式执行订单。这种算法应该被编程为跟踪市场的关键数据，例如当前的交易量、价格和一天中的时间。根据这些信息，计算机将释放股票，以便在及时移动整个交易的同时获得尽可能最好的交易。

One way to manage the sale of a large block of trades is to employ an automated trading algorithm that executes the orders in a reasonable manner. Such an algorithm should be programmed to track key data from the market, such as the current trading volume, price, and time of day. Based on this information, the computer will release the shares so as to get the best deals possible consistent with moving the entire block in a timely manner.

催化闪电崩盘的公司使用了这样的算法。当然，魔鬼藏在细节中，而在这个案例中确实存在魔鬼。该公司的算法有一个简单的规则：向市场输入订单，使这些订单占前一分钟总交易量的 9% 以下。请注意，该算法完全忽略了交易价格。话虽如此，在某种程度上，这并不是一个完全荒谬的算法，因为通常交易量是市场流动性的良好指标，而流动性与稳定的价格息息相关。理论上，如果你仍然是市场的一小部分（这里指不到 9%）并且如果市场以“正常”方式运作，该算法应能产生稳定合理的价格。本质上，该算法搭了来自市场的成交量信息的便车，并将其用作合理价格的代理。通过这样做，它避免了对何时出售做出任何困难的预测。

The firm that catalyzed the flash crash used such an algorithm. Of course, the devil is in the details, and in this case there was a devil indeed. The firm’s algorithm had one simple rule: feed in orders to the market so that these orders constitute less than 9 percent of the overall trading volume during the previous minute. Note that this algorithm completely ignores the trading price. That being said, at some level it is not a completely absurd algorithm, as normally volume is a good indicator of the market’s liquidity, and liquidity is tied to stable prices. In theory, if you remain a small part of the market (here, less than 9 percent) and the market is functioning in a “normal” way, this algorithm should result in stable and reasonable prices. In essence, the algorithm hitches a free ride on the volume information coming from the market and uses this as a proxy for reasonable prices. By doing so, it avoids having to make any difficult predictions about when to sell.

不幸的是，最近交易中发生了两个变化，使得这种基于交易量的代理变得非常危险。首先，衍生证券的兴起将各个市场联系在一起。E-minis 与标准普尔 500 指数挂钩。还有其他设计略有不同的衍生品，例如标准普尔存托凭证（称为 SPDR 或“Spiders”，交易代码为 SPY），也与该指数挂钩。如果其中一种衍生品的价格与其他衍生品相差很大，那么就有套利机会锁定利润，无论基础价格如何变化，通过出售较昂贵的证券并购买较便宜的证券来弥补之前的销售。另一种套利机会将衍生品市场与更广泛的市场联系起来：鉴于衍生品的价格与一组个股（构成指数）挂钩，每当该组股票的价格与相关衍生品的价格不同时，你都可以通过卖出（或买入）基础股票来抵消衍生品的买入（或卖出）从而获利。

Unfortunately, there have been two recent changes in trading that have made this volume-based proxy quite dangerous. First, the rise of derivative securities has interconnected various markets. E-minis are linked to the S&P 500 Index. There are other derivatives with slightly different designs, such as S&P Depositary Receipts (known as SPDRs or “Spiders” and traded under the ticker symbol SPY), that are also tied to this index. If the price of one of these derivatives differs substantially from the others, there is an arbitrage opportunity to lock in a profit, regardless of what happens to the underlying prices, by selling the more expensive security and buying the cheaper one to make good on the previous sale. An alternative arbitrage opportunity interconnects the derivatives market to the broader markets: given that the price of the derivatives is tied to a bundle of individual stocks (which make up the index), you can always make a profit by offsetting the purchase (or sale) of the derivative by selling (or buying) the underlying bundle of stocks whenever the price of that bundle differs from the price of the associated derivative.

后者的机会得益于我们在市场上看到的第二个重大变化，即获取大量证券和市场的交易条件信息，计算潜在机会，并执行任何所需的交易，所有这一切都在眨眼之间完成。交易的这场革命源于计算机的兴起，事实上，现在事情发生的速度远快于眨眼（眨眼需要 350 毫秒，而电子可以在这段时间内传播超过 65,000 英里）。

This latter opportunity is facilitated by the second major change we have seen in markets, namely, the ability to get information about the trading conditions across a vast array of securities and markets, calculate potential opportunities, and execute any needed trades, all in the blink of an eye. This revolution in trading is due to the rise of the computer and, indeed, things now happen far faster than the blink of an eye (which takes a somewhat poky 350 milliseconds, a length of time in which an electron can travel more than 65,000 miles).

高度互联的市场和快速进行的交易相结合，形成了一种十年前还未曾预见到的新型复杂系统。一个市场的交易会在其他市场产生反响，因为它引发的各种不一致会得到纠正。当然，这些纠正可能会引发自己的反响。如果来自各种连接的（非预期）反馈回路是负面的，系统中的反响会慢慢消失，随着价格重新调整，市场体验会更好。然而，如果反馈回路是正的，我们最终会看到反响相互放大，产生类似于麦克风离扬声器太近时听到的刺耳声音。

The combination of highly connected markets and quickly conducted trades has formed a new kind of complex system unforeseen even a decade ago. A trade in one market reverberates across the others, as the various inconsistencies it induces get corrected. Of course, those corrections can start their own reverberations. If the (unintended) feedback loops emerging from the various connections are negative, the reverberations in the system slowly die out, and the markets are better for the experience, as prices realign with one another. If, however, the feedback loops are positive, we end up with the reverberations amplifying one another, creating something akin to the horrible screeching sound we hear when a microphone is held too close to a loudspeaker.

过去几年，市场上出现了一种新型交易公司：高频交易商 (HFT)。这些公司完全拥抱了信息时代，并创建了算法交易商，这些交易商可以监视市场并在极短的时间内执行任何理想的交易。对于这种类型的交易，获得买入或者在其他人之前将信息卖给交易所是如此重要，以至于你的计算机硬件的物理位置等因素都很重要——电子每纳秒传播大约一英尺，因此每靠近交易所的机器一英尺，你就会比竞争对手多一纳秒的优势。

Over the past few years, a new kind of trading firm has arisen on the market scene: the high-frequency trader (HFT). These firms have fully embraced the information age and have created algorithmic traders that watch over markets and execute any desirable trades on a remarkably short time scale. For this type of trading, getting your buy or sell message to the exchange before anyone else is so important that factors such as where you physically locate your computer hardware matter—an electron travels about a foot each nanosecond, so every foot closer to the exchange’s machines gives you a nanosecond advantage over your competitors.

高频交易员现在的交易量非常大。一般来说，他们不喜欢一次持有太多股票。因此，虽然他们可能会买入很多，但也会卖出很多，所以最终（尽管新的现实是，在全球互联互通的市场中，一天真的没有结束），他们对任何特定证券的净持股量都很小。

HFTs now account for an enormous volume of trades. In general, they don’t like holding too many shares at any one time. Thus, while they might buy a lot, they also sell a lot, so at the end of the day (though the new reality is that with global, interconnected markets, there really is no end of the day) their net holdings of any given security are small.

高频交易的存在无疑改变了市场的动态。20 世纪 80 年代末，在圣菲研究所，我的同事理查德·帕尔默、约翰·鲁斯特和我创建了“双重拍卖锦标赛”，以测试一些有关市场的核心思想。学者、专业交易员和感兴趣的业余爱好者在网上测试他们的交易策略（据我们所知，这是第一次基于互联网的拍卖），然后将最终版本提交给我们进行分析。

The existence of HFTs certainly alters the dynamics of markets. In the late 1980s at the Santa Fe Institute, my colleagues Richard Palmer, John Rust, and I created the Double Auction Tournament to test some core ideas about markets. Academics, professional traders, and interested amateurs tested their trading strategies over the web (to our knowledge, this was the first Internet-based auction) and then submitted final versions to us for analysis.

我们感兴趣的一个问题是，在由机器和人类交易员组成的混合市场中会发生什么。当我们在不补偿人类和机器之间固有的速度差异的情况下运行这样的市场时，我们发现，当市场开盘时，机器会在人类做出反应之前进行大量交易。在那之后，机器只是静静地待在后台，而人类则在彼此交易，仅当人类提出糟糕的报价时才会激活，在这种情况下机器会进入市场并窃取交易。

One of our interests was what would happen in a hybrid market composed of both machine and human traders. When we ran such a market without any compensation for the innate speed differences between humans and machines, we found that when the market opened there was a flurry of trades by the machines before the humans could even react. After that point, the machines just stayed quietly in the background as the humans traded with each other, activating only when a human made a bad offer, in which case a machine would jump into the market and steal the deal.

有人猜测，我们当前的市场系统（既有人类交易员，也有高频交易员）可能与混合型双重拍卖锦标赛的行为方式类似。高频交易员独特的速度优势可能导致机器交易的激增，而机器则在较为平静的时期内待在后台，等待利用人类错误。当我们消除机器的速度优势时，人类和机器很容易共存，根据数据很难区分，唯一的例外是，人类倾向于提出以零或五结尾的报价，而机器则没有那么受限制。

One suspects that our current market system, with both human traders and HFTs, may behave in an analogous way to the hybrid Double Auction Tournament. HFTs’ distinct speed advantages may be causing flurries of machine trading, punctuated by quieter periods where the machines remain in the background waiting to take advantage of human errors. When we eliminated the speed advantages of the machines, humans and machines easily coexisted and were difficult to tell apart given the data, with the one exception being that humans tended to place offers that ended in digits of either zero or five, while machines were not so constrained.

回到 5 月那个决定命运的日子，下午 2:32，我们的交易员大概按下了回车键，以响应一些听起来无害的提示，例如“您确定要执行这些交易吗？”，然后一块石头落入市场池塘，引起了一丝涟漪。随着高频交易员和其他中介机构购买新提供的合约，市场能够吸收初始交易量。在接下来的十分钟内，高频交易员积累了相当多的合约，为了平衡他们的头寸，他们开始抛售。一场高风险的烫手山芋游戏随之而来，高频交易员开始相互买卖，合约只是偶尔泄露给其他市场参与者。

Returning to that fateful day in May, at 2:32 p.m. our trader presumably pushed the enter key in response to some innocuous-sounding prompt along the lines of “Are you sure you want to execute these trades?” and a stone was dropped into the market pond, causing a small ripple. The market was able to absorb the initial trade volume, as HFTs and other intermediaries bought the newly offered contracts. Over the next ten minutes, the HFTs accumulated quite a few of these contracts, and in order to balance out their positions, they began to sell. A game of high-stakes hot potato ensued, in which the HFTs began to buy and sell to one another, with only occasional leaks of the contracts out to other market participants.

正是在此时，算法的致命缺陷开始显现。烫手山芋游戏开始产生大量的市场交易量，在很短的时间内交易了超过 100,000 股。该算法除了交易量之外，对其他一切都视而不见，认为这种活动的增加是市场流动性强、价格稳定的信号，并开始向已经不稳定的组合中投入更多股票。这一新行动进一步破坏了市场稳定，因为 E-mini 股票的任何实际流动性都枯竭了，价格开始暴跌。在按下回车键后的十三分钟内，该算法卖出了 35,000 份合约，剩下的 40,000 份合约在短短七分钟内售罄。因此，最初的 75,000 份合约在不到二十分钟内全部售出——而在过去，使用更标准的算法，处理类似规模的合约需要大约六个小时。毫不奇怪，最初的交易和后续活动导致 E-mini 合约价格大幅下跌（见图 3.2）。

It is at this point that the fatal flaw in the algorithm becomes apparent. The game of hot potato started to generate a lot of market volume, with more than 100,000 shares being exchanged in a very short time. The algorithm, blind to everything but the volume, saw this increased activity as a sign that the market was liquid and that prices were stable, and it began to dump even more shares into an already volatile mix. This new action destabilized things even further, as any real liquidity in the E-mini shares dried up and the prices began to plummet. In the thirteen minutes after the enter key was pressed, the algorithm sold 35,000 contracts, and the remaining 40,000 contracts were sold off in a scant seven minutes more. Thus, all of the initial 75,000 contracts were sold in under twenty minutes—whereas in the past, using more standard algorithms, it had taken around six hours to dispose of similarly sized lots. The initial trades and subsequent activity, not surprisingly, resulted in a substantial drop in the price of the E-mini contracts (see Figure 3.2).

然而，下午 2:45:28 发生的一件事可能阻止了一场更严重的灾难。当时，一个自动机制暂停了交易五秒钟。该机制由交易所实施，旨在识别市场条件，在这种条件下，进一步的交易会导致价格异常大幅波动。虽然五秒钟似乎微不足道，但在纳秒统治的时代，这却是永恒。这段时间足够让其他交易者进入市场，让事情走上正轨复苏。在接下来的二十三分钟内，更加关注基本面的买家开始涌入市场，价格出现反弹。

However, at 2:45:28 p.m. an event happened that likely prevented an even deeper disaster. At that time, an automated mechanism paused trading for five seconds. This mechanism had been put in place by the exchange, and it was designed to recognize market conditions in which the execution of further trades would result in unnaturally large price swings. While five seconds seems like an inconsequential amount of time, it is an eternity in an era when nanoseconds rule. It was long enough to allow other traders to enter the market and get things on the road to recovery. Over the next twenty-three minutes, buyers with a more fundamental focus began to flood the market, and prices rebounded.

图 3.2： 2010 年 5 月 6 日 E-mini 合约的价格与交易量。（来源：美国证券交易委员会。）

Figure 3.2: The price and volume of E-mini contracts on May 6, 2010. (Source: US Securities and Exchange Commission.)

E-mini 市场行为不良的直接原因很容易与交易算法的缺陷联系起来。通过将交易数量与交易量联系起来，算法中无意中嵌入了一个正反馈循环：如果初始交易导致交易量大幅增加，那么算法会进行更多交易，这将进一步增加交易量。如果没有高频交易，幼稚的交易算法可能不会引发足够多的额外交易来触发反馈循环。然而，随着高频交易者的快速交易和他们维持相对中立的股票头寸的愿望，一种新的市场动态形成了，在系统中嵌入了一个正反馈循环。

The proximate cause of the bad behavior in the E-mini market is easily tied to the flaw in the trading algorithm. By linking the number of trades to only volume, a positive feedback loop was unintentionally embedded in the algorithm: if the initial trades cause a big increase in volume, then the algorithm trades even more, which will further increase volume. If the HFTs had not been in the picture, the naive trading algorithm might not have induced enough extra trades to trigger the feedback loop. However, with the rapidly trading HFTs and their desire to maintain relatively neutral share positions, a new market dynamic formed that embedded a positive feedback loop into the system.

如果这只是 E-mini 市场的故事，那么它就值得作为一个寓言来讲述，讲述算法（实际上是人类）的傲慢以及意外后果和正反馈的危险。但故事并没有就此结束。

If this were just the story of the E-mini market, it would be worth telling as a parable about algorithmic—actually, human—hubris and the dangers of unintended consequences and positive feedback. But the story does not end here.

鉴于市场的相互关​​联性，E-mini 市场的情况不会就此结束。随着 E-mini 价值的下跌，交易员开始在其他地方寻找套利机会——在这种情况下，要么在 SPDR 中，要么在构成指数本身的股票中。在正反馈循环的推动下，E-mini 的价格迅速下跌，而 SPDR 和构成指数的股票的价格变动则要慢得多。这创造了一个新的获利机会，即通过购买相对便宜的 E-mini 并以 SPDR 或基础股票组合的形式出售其更昂贵的等价物。

Given the interconnectedness of markets, what happens in the E-mini market does not stay there. As the E-mini declined in value, traders started to look for arbitrage opportunities elsewhere—in this case, either in SPDRs or in the stocks that make up the index itself. While the E-mini’s price was rapidly declining, driven by the positive feedback loop, the prices of SPDRs and the stocks that formed the index moved much more slowly. This created a new opportunity to profit by buying the relatively cheap E-minis and selling their more expensive equivalents in the form of SPDRs or the bundle of underlying stocks.

在运作良好的市场体系中，E-minis 崩盘带来的套利机会通常会抑制价格动态。套利者的牟利活动会提高 E-mini 的价格（考虑到新发现的购买需求）并降低 SPDR 或捆绑产品的价格（考虑到新发现的出售欲望），价格会重新调整并消除获利套利的机会。不幸的是，由于先前存在的动荡和正反馈循环，市场未能迅速调整，套利机会仍然存在。这导致其他市场的交易压力，它们也开始侵蚀各自的订单簿。此外，新产生的混乱让许多潜在的做市商感到紧张，因为传入的数据流中没有任何东西可以解释观察到的巨大价格变化——此时由于大量交易的涌入，这些数据流已经开始出现问题。这触发了数据完整性检查，公司暂停了交易活动。其他公司完全退出市场，因为持续监控公司头寸和潜在金融风险的自动系统开始超过预设限制并停止了公司的交易。最后，在一些公司，监督所有这些奇怪活动的人只是失去了勇气（或表现得很明智），并从市场上撤回了他们的报价。

In a well-functioning market system, the arbitrage opportunities created by the collapsing E-minis would normally dampen the price dynamics. The profit-seeking activities of the arbitrageurs would raise the price of the E-mini (given the newfound demand to buy) and lower the price of the SPDR or bundle (given the newfound desire to sell), and the prices would realign and remove the opportunity for profitable arbitrage. Unfortunately, given the preexisting turmoil and the positive feedback loop, the markets failed to realign very quickly, and the arbitrage opportunity remained. This resulted in trading pressure on the other markets, and they started to eat into their respective order books as well. Moreover, the newly generated chaos made many potential market makers nervous, as nothing in the incoming data streams—which by this time were starting to falter given the massive influx of trading—could account for the large price changes being observed. This triggered data integrity checks, where firms paused their trading activity. Other firms withdrew entirely from the market as automatic systems that continuously monitor a firm’s position and potential exposure to financial risk began to exceed preset limits and halted the firm’s trading. Finally, in some firms, humans overseeing all of this bizarre activity simply lost their nerve (or behaved wisely) and withdrew their offers from the market.

随着做市商的退出，订单簿开始清空，只剩下长期订单，在极端情况下，自动“存根”订单被设定在荒谬的价格点，只是为了确保总有人愿意买卖任何特定股票。因此，确实发生的交易价格随着时间的推移变得越来越极端。超过三百只股票的价格变化高达 60%（超过 20,000 笔交易，共计 550 万股，在这种极端情况下执行）。在最极端的情况下，证券按照其原始价格进行交易，一些股票售价为一美分，而其他股票则售价为10万美元。

As the market makers withdrew, the order books began to empty out, leaving only long-standing orders and, at the extremes, automated “stub” orders set at ridiculous price points just to ensure that there would always be someone willing to buy or sell any given share. Thus, the transactions that did occur were happening at prices that became more and more extreme over time. More than three hundred stocks experienced price changes of as much as 60 percent (more than 20,000 trades, constituting 5.5 million shares, were executed at such extremes). At the most extreme, securities were traded at their stub prices, with some shares going for a penny and others for $100,000.

2010 年 5 月 6 日事件的后果十分严重。短期内，人们意识到这些事件与交易所希望监管的“公平有序”市场相去甚远，交易所中断了与混乱开始前的价格相差甚远的交易，因为这些交易被认为是“明显不切实际的价格”，考虑到严峻的市场状况，这些价格是“明显错误的”。虽然交易所一直有权中断此类交易（请务必阅读细则），但用于确定“明显错误”的实际机制尚未明确定义，这促使该领域进行了改革。第二次重大改革改变了各种熔断机制的部署方式。个别市场通常有专门设计用于在出现意外情况时停止交易的机制，在实践中，即使是非常短暂的暂停也能让市场迅速稳定下来并有序恢复。不幸的是，即使存在熔断机制，也可能产生意想不到的后果，因为给定证券的多次暂停可能会导致做市商撤回其流动性。此外，鉴于全球连通性以及许多交易相同证券的市场，一个市场的交易暂停可能会将转移的交易转移到另一个市场，从而绕过最初的中断因素并加剧问题。

The aftermath of the events of May 6, 2010, was significant. In the short term, there was a realization that the events were far from the “fair and orderly” markets that the exchanges want to oversee, and the trades that took place far from the prices prevailing just before the chaos began were broken by the exchanges, as they were considered “clearly unrealistic prices” that were “clearly erroneous” given the severe market conditions. While exchanges have always had the power to break such trades (always read the fine print), the actual mechanisms used for determining “clearly erroneous” were not well defined, and this has prompted a reform in this area. The second major reform has altered how various circuit breakers get deployed. Individual markets often have mechanisms designed to halt trading when unexpected conditions arise, and in practice, even very short halts have allowed markets to stabilize quickly and resume in an orderly fashion. Unfortunately, even the existence of circuit breakers can have unintended consequences, as multiple halts in a given security might cause market makers to withdraw their liquidity. Also, given global connectivity and many markets trading the same security, a trading halt in one market might just shift the displaced trades to another market, circumventing the original breaker and exacerbating the problem.

尚未改革的一个领域是限制高频交易。例如，由高频交易引起的反馈回路可以通过征收交易税或重新设计市场来抑制高频交易，以降低纳秒级速度的重要性。

The one area that has not been reformed is limiting the HFTs. For example, the feedback loops induced by the HFTs could be dampened by imposing transaction taxes or redesigning markets to lessen the importance of nanosecond-scale speed.

即使上述修复措施也无法解决导致闪电崩盘的根本问题。我们在不知不觉中创建了一个复杂的自适应金融系统，我们既无法理解也无法控制。在其创建的每个阶段，我们都以增加利益的名义增加了额外的复杂性：将市场相互连接将确保价格差异迅速消除，拥有高频交易者将保证任何交易都有现成的交易伙伴，使用衍生品将为农民提供对冲恶劣天气风险的手段，为养老基金提供为其投资组合投保的手段，等等。虽然这些单独的部分都有意义，但集合起来可能就没意义了。

Even the above repairs do not address the fundamental problem that caused the flash crash. We have unknowingly created a complex adaptive financial system that we do not understand and cannot control. At each stage of its creation, we have accrued additional complexity in the name of added benefits: connecting markets with one another will ensure that price discrepancies will be eliminated quickly, having high-frequency traders will guarantee a ready trading partner for any transaction, using derivatives will provide a means for farmers to hedge the risks of bad weather and for pension funds to insure their portfolios, and so on. While each of these individual pieces makes sense, the collection may not.

正如我们已经看到的，还原论并不意味着建构论。因此，尽管系统中的任何单个部分的动机和理解可能是合理的，但这不应该让我们对整体的行为有任何信心。闪电崩盘不是故意而为的，而是自然而然发生的。

As we have already seen, reductionism does not imply constructionism. Thus, while the motivation for, and understanding of, any single piece in the system may be sound, that should not give us any confidence in the behavior of the whole. The flash crash occurred not by design but through emergence.

闪电崩盘是一个令人惊讶的温和警告，我们必须注意。5 月那 30 分钟内发生的事件虽然引人注目，但却是可以逆转的。虽然仔细剖析戏剧性事件很有用，但我们需要首先防止尸体的出现。不幸的是，闪电崩盘向我们表明，无论多么好尽管我们的回顾性调查可能很有限，但我们的前瞻性知识却很薄弱。我们甚至无法开始理解我们所建立的金融体系的含义。

The flash crash was a surprisingly gentle warning that we must heed. The events during that thirty-minute period in May, while striking, were reversible. While careful autopsies of dramatic events are useful, we need to be in a position to prevent the appearance of the bodies in the first place. Unfortunately, the flash crash has shown us that, however good our retrospective investigations might be, our prospective knowledge is weak. We can’t even begin to grasp the implications of the financial systems we have built.

虽然闪电崩盘是因贪婪而导致的，但幸运的是，它涉及的是无知，而不是恶意。想象一下，如果涉及恶意和更多的深思熟虑，可能会造成多大的混乱和长期破坏。比如说，一个恐怖组织或流氓国家要渗透到我们市场的基础计算机或人工系统，造成更大、更持久的破坏，会有多难？这似乎并不难。对网络基础设施的攻击似乎是可能的，例如破解交易所的实际系统或众多分散交易业务的系统，或者以某种方式破坏或改变指导或报告交易的通信流，尤其是考虑到像 Stuxnet 计算机蠕虫这样的例子，它阻碍了伊朗的铀浓缩能力。与金融机构相关的人工系统也很容易受到攻击。事实上，有些例子表明，单个交易员的行为导致整个机构倒闭，例如 1995 年成立 233 年的巴林银行倒闭。因此，将一个或多个交易员插入系统，并有足够的权限访问交易柜台，以发起精心协调的恶意攻击是可行的。一种更雄心勃勃的方法可能包括建立一个看似合法的基金或高频交易业务，获得特权和不受限制的交易系统访问权限，或者，如果这太麻烦，只需执行大量合法交易者之间同时进行的交易。这种攻击的影响很难预测，但至少会严重削弱信心，而且后果可能更为严重，导致确保我们经济生存的市场部分崩溃。

While the flash crash was driven by greed in the pursuit of profit, it fortunately involved ignorance, not malice. Imagine the chaos and long-term devastation that could happen if malice and a bit more forethought were involved. How difficult would it be for, say, a terrorist organization or rogue state to infiltrate either the computer or human systems that underlie our markets and wreak havoc on a much larger, and longer-lasting, scale? This does not seem all that hard. Attacks on the cyber infrastructure, such as cracking the actual systems of the exchange or those of the numerous decentralized trading operations, or somehow disrupting or altering the communication flows that direct or report trades, seem possible, especially given examples such as the Stuxnet computer worm, which hampered Iran’s ability to enrich uranium. The human systems connected with financial institutions are also vulnerable. Indeed, there are examples where the actions of a single trader brought down an entire institution, as with the fall of the 233-year-old Barings Bank in 1995. Thus, inserting one or more traders into the system with enough access to the trading desks to launch a carefully coordinated, malicious attack is feasible. A more ambitious approach might include setting up an apparently legitimate fund or HFT operation that gets privileged and unfettered access to the trading systems, or, if that is too bothersome, simply executing a large number of simultaneous transactions spread across legitimate traders. The impact of such an attack is hard to predict, but at the very least it would seriously erode confidence, and it could be far more consequential, leading to a partial collapse of the very markets that ensure our economic survival.

不幸的是，闪电崩盘所蕴含的故事可能并非独一无二。事实上，2008 年开始的最近全球金融危机也有类似的意味。

Unfortunately, the story encapsulated in the flash crash may not be all that unique. Indeed, the recent worldwide financial collapse that started in 2008 has similar undertones.

2008 年金融危机的核心是一场全面涵盖了七宗罪的经济危机。贪婪的固定收益资产买家为了获得略高的回报，愿意购买新成立的担保债务凭证。奢侈的购房者希望房价上涨能让他们在未来进行再融资，因此选择购买房屋，并大幅增加抵押贷款支付额，远远超出了他们目前的能力范围。贪婪的抵押贷款经纪人可以将可疑的抵押贷款转嫁给创建并迅速出售抵押贷款支持证券的公司，他们愿意让几乎所有买家都有资格购买。嫉妒的公司为了提高利润，开始利用自身杠杆，同时向客户推销可疑的衍生品。懒惰的评级机构依靠公司的口碑和过时的统计模型，在收取佣金的同时，对新证券给出了荒谬的高评级。骄傲的政府机构对房屋所有权的增长和不受监管的市场的力量津津乐道，袖手旁观。至于愤怒，地狱的愤怒不会像被蔑视的复杂经济体系那样强烈。

At the heart of the 2008 financial collapse was an economic crisis that fully embraced all of the seven deadly sins. Gluttonous fixed-income-asset buyers, for the promise of slightly higher returns, were willing to buy up newly formed collateralized debt obligations. Extravagant home buyers, hoping that rising house prices would allow refinancing in the future, opted for houses and ballooning mortgage payments well beyond their current means. Greedy mortgage brokers, able to pass on even suspect mortgages to firms that created and quickly sold off mortgage-backed securities, were willing to qualify almost any buyer. Envious firms, wanting to boost their bottom lines, began leveraging themselves while marketing suspect derivatives to their customers. Slothful rating agencies, relying on the word of the firms and outdated statistical models, gave absurdly high ratings to novel securities while collecting commissions. Prideful government agencies, relishing the increase in home ownership and the power of the unregulated market, stood idly by. As for wrath, hell hath no fury like a complex economic system scorned.

上一段的目的不是讲述一些现代道德故事，而是强调在系统的每个层面上，相关实体如何遵循完全可以理解的（尽管可能不是道德的）激励机制。因此，从非常实际的意义上讲，经济学家和政策制定者完全有能力了解系统的每个部分。不幸的是，正如我们之前所看到的，认为了解系统的各个部分就意味着了解整个系统是一种经常犯的错误。

The point of the previous paragraph is not to tell some modern morality tale but rather to emphasize how, at each level of the system, the entities involved were following perfectly understandable—though perhaps not virtuous—incentives. Thus, in a very real sense, economists and policy makers were fully equipped to understand each part of the system. Unfortunately, as we have seen before, thinking that understanding the parts of a system implies that you understand the whole system is a sin that is committed all too often.

正如我们在闪电崩盘案例中看到的那样，正反馈机制将小事件放大为大事件。房地产市场充斥着正反馈。如果抵押贷款变得更容易获得，房屋需求就会上升，从而导致房价上涨。房价上涨使得贷款人更愿意发放抵押贷款，因为房价上涨确保有足够的抵押品来降低贷款风险。

As we saw in the case of the flash crash, positive feedback mechanisms amplify small events into large ones. The housing market is rife with positive feedbacks. If mortgage money becomes easier to get, the demand for houses goes up, resulting in higher house prices. These higher house prices make lenders more willing to grant mortgages, as rising prices ensure that sufficient collateral exists to lower the risk of the loans.

在美国房地产市场，正反馈往往会强化系统的每个部分。更高的房价鼓励了更多的买家，降低了贷款标准，并导致了风险更低的衍生品和更宽松的政府政策，而这些因素相互反馈，强化了连锁效应。可惜的是，在上升过程中放大系统的力量，在下降过程中加速了系统的崩溃。不幸的是，与闪电崩盘不同，在金融崩溃期间几乎没有设置熔断机制或类似的东西。

In the US housing market, the positive feedbacks tended to reinforce every part of the system. Higher house prices encouraged more buyers, lowered lending standards, and resulted in less risky derivatives and easier government policies, and each of these fed back on the others, reinforcing the chain of effects. Alas, the same forces that amplified the system on the way up accelerated its demise on the way down. Unfortunately, unlike with the flash crash, there were few circuit breakers, or anything like them, in place during the financial collapse.

系统各部分之间的相互作用和联系在这里至关重要。想象一下与金融危机相关的任何关键市场，它们都是雷击多发山脊上的木材农场。时不时地，雷击中一棵树，如果击中一棵树，那棵树就会起火并点燃附近的树木。如果你想最大限度地提高木材产量，你必须在种植更多树木以获得更多木材和保持土地休耕以控制附近火灾之间做出权衡。这里的最佳选择取决于各种潜在因素，例如雷击频率和树木的生长速度，但是否做出最佳选择取决于谁拥有山脊。如果一个人拥有山脊，那么建立几条防火带对她有利，这样一星火花就不会导致大火烧毁整个山脊。不幸的是，在每个潜在树木种植地由不同的人按照自己的动机拥有的系统中，可能不会出现这样的防火带。在这种情况下，虽然所有个人都会从防火带的建设中受益，但没有人愿意成为提供防火带的人，因为她将没有木材可采伐。从经济角度来看，防火带建设不足，这导致火灾破坏性远大于协调机制下可能达到的水平，采伐量也远低于协调机制下可能达到的水平。

The interactions and connections among the various parts of the system are critical here. Imagine any of the key markets associated with the financial collapse as a timber farm along a lightning-prone ridge. Every now and then, lightning strikes, and if it hits a tree, that tree goes up in flames and ignites any neighboring trees. If you want to maximize the timber harvest, you must make a trade-off between growing more trees to get more timber and keeping land fallow to contain neighboring fires. The best choice here depends on various underlying factors, such as the frequency of lightning and the growth rate of trees, but whether the best choice gets made depends on who owns the ridge. If a single person owns the ridge, it will be in her interest to include a few firebreaks, so that a single spark won’t lead to a conflagration that takes out the entire ridge. Unfortunately, such firebreaks may not arise in a system where each potential tree site is owned by a different individual following her own incentives. In this situation, while all individuals would benefit from the inclusion of firebreaks, no individual wants to be the person who provides the firebreak, since she would have no timber to harvest. In economic terms, firebreaks are underprovided, and this results in far more destructive fires and much lower harvests than are possible under a more coordinated regime.

金融危机爆发之初，抵押贷款市场就是如此。没有哪个实体愿意放弃任何可能的交易，从而损失一些即时利润。因此，一家银行发现持有另一家银行发行的证券对个人有利可图，即使那家银行已经从另一家银行购买了证券，依此类推，直到一家非常遥远的银行破产都可能导致整个承诺体系瓦解。同样，一家公司可能会同时购买和出售类似保险的违约风险保单（称为信用违约掉期），并认为其地位是安全的，因为任何一项保单的损失都将被另一项保单的收益完美抵消。然而，如果一家公司在违约时未能履行支付义务（想想美国国际集团，又名 AIG），整个系统就会崩溃。在这些以及无数其他情况下，重要的是由个体合理但整体不合理的安排产生的联系链。如果没有良好的防火措施，这些系统很容易受到小事件的影响，从而产生灾难性的后果。

So it was with mortgages at the start of the financial crisis. No entity wanted to forgo any possible trade and lose some immediate profit. Thus, a single bank finds it individually profitable to hold securities issued by another bank, even though that other bank has bought securities from another bank, and so on down the line, to the point where the failure of a very distant bank can cause the whole system of promises to unravel. Similarly, a single firm may simultaneously buy and sell insurance-like policies on the risk of default (known as credit default swaps) and feel that its position is safe, since any loss to one of the policies will be perfectly offset by a gain to the other. However, if one firm fails to meet its obligation to pay in the case of a default (think American International Group, aka AIG), the entire system unravels. In these and countless other situations, what is important here is the chain of connections that results from individually rational, but globally irrational, arrangements. Without well-placed firebreaks, these systems are subject to small events having catastrophic consequences.

在 2008 年金融危机和闪电崩盘中，我们都看到曾经生机勃勃、蓬勃发展的系统突然变得沉寂。这种转变发生在各种复杂系统中。例如，一个生物体处于动态状态，其许多相互作用的部分形成了一个生机勃勃、强健的生物体。现在，如果引入一个适当的冲击，曾经生机勃勃的生物体就会进入死亡状态，其所有部分都不会相互作用。不幸的是，这也是一种强健的状态。

In both the 2008 financial collapse and the flash crash, we saw systems that were vital and thriving at one moment suddenly become quiescent. This type of switching happens in a variety of complex systems. For example, a living organism exists in a dynamic state where its many interacting parts result in a vital and robust organism. Now introduce, say, a well-placed shock, and the once vital organism is pushed into a death state where none of its parts interact. Unfortunately, this too is a robust state.

预期通常能使社会系统（尤其是市场）运转。预期可能导致自我实现的预言，无论是好是坏。因此，在闪电崩盘中，一旦流动性枯竭，做市商的预期可能会变化到他们认为将无法再找到合理的交易伙伴的地步，这导致他们撤回订单并实现预期，进一步加剧流动性危机。一旦房地产泡沫开始破裂，房价的下跌会改变贷款人的预期，他们会对在没有极高抵押水平的情况下发放新的（或为旧的）抵押贷款持谨慎态度，这反过来又导致价格下跌，新形成的预期得到强化。在这两种情况下，与预期有关的反馈回路都会加剧糟糕的情况。

Expectations often keep social systems, and especially markets, operating. Expectations can lead to self-fulfilling prophecies, both good and bad. Thus, in a flash crash, once liquidity dries up, the expectations of market makers may change to the point where they believe they will no longer be able to find reasonable trading partners, which causes them to withdraw their orders and realize their expectations, further exacerbating the liquidity crisis. Once a housing bubble begins to pop, the downward spiral of house prices alters the expectations of the lenders, and they become wary of granting new (or refinancing old) mortgages without extreme levels of collateral, which in turn causes prices to fall and the newly formed expectations to be reinforced. In both cases, feedback loops concerning expectations exacerbate a bad situation.

当“涌现”对你有利时，亚当·斯密的“看不见的手”是一件奇妙的事情。如果“涌现”只在带来好事时出现，生活会更有趣，尽管不那么有趣。不幸的是，我们已经看到了“涌现”的阴暗面，一个看似无害的事件引发了连锁反应，最终导致灾难。复杂系统，无论是有意还是无意的，都在我们的世界中扮演着越来越重要的角色。虽然我们可能永远无法完全控制这样的系统，但我们可以通过巧妙地引入隐喻性的防火墙（如金融市场中使用的断路器）来减轻它们的负面影响。我们对如何创建此类控制的理解远远落后于我们实施它们的需求，我们必须迅速发展这种知识，这样王国才不会因为缺少一颗钉子而失去。

When emergence is working for you, the invisible hand of Adam Smith is a wonderful thing. Life would be a lot more fun, albeit much less intriguing, if emergence arose only when it led to good things. Unfortunately, we have seen the dark side of emergence, in which a seemingly innocuous event triggers a cascade that leads to disaster. Complex systems, whether intentional or not, are playing an increasingly important role in our world. While we might not ever be able to fully control such systems, we may be able to mitigate their downsides through the clever introduction of metaphorical firebreaks such as the circuit breakers that are used in financial markets. Our understanding of how to create such controls is lagging well behind our need to implement them, and we must quickly develop this knowledge so that the kingdom won’t be lost for want of a nail.

四

Four

从一到多：异质性

From One to Many: Heterogeneity

一枚魔戒统治他们所有人，一枚魔戒找到他们，

One Ring to rule them all, One Ring to find them,

一枚戒指将他们全部带走，并将他们束缚在黑暗中。

One Ring to bring them all and in the darkness bind them.

—— JRR 托尔金，《护戒使者》

—J. R. R. Tolkien, The Fellowship of the Ring

埃经济学家们喜欢“代表代理人”，这是一种理论惯例，它使数学变得容易得多。代表代理人背后的想法是，我们不必担心经济中的每个消费者，而是可以用一个消费者来代表所有人——一个代理人来统治所有人。显然，这样的假设大大简化了最终的模型，因为代表代理人可以代表这种方法适用于大量个性古怪的消费者，他们可能很难逐一追踪。事实上，理论经济学家和政策制定者经常在影响数亿人生活的模型中使用这种技巧。只要个人行为平均下来是合适的，使用这种方法似乎是显而易见的选择。

Economists are fond of the “representative agent,” a theoretical convention that makes the math much, much easier. The idea behind the representative agent is that instead of having to worry about, say, every consumer in the economy, we can substitute a single consumer to represent everyone—one agent to rule them all, as it were. Obviously, such an assumption greatly simplifies the resulting model, as the representative agent can stand in for a vast horde of individually quirky consumers who might be difficult to track one by one. Indeed, theoretical economists and policy makers often use such a trick in models that influence the lives of hundreds of millions. As long as individual behaviors average out appropriately, using such an approach seems like an obvious choice.

我们是否可以使用代表性代理来模拟复杂系统，实际上是一个关于异质性是否重要的​​问题。如果异质性不重要，那么假设以代表性代理的形式体现的平均行为就足够了：由一群参与者建模的系统与由单个代表性代理组成的系统将出现相同的行为。如果异质性确实重要，那么我们需要一种新的方法来理解、预测和控制我们的世界。

Whether we can use representative agents to model complex systems is really a question about whether heterogeneity matters. If it doesn’t matter, then assuming average behavior embodied in the form of a representative agent suffices: the same behavior will emerge from a system modeled by a population of actors as from one consisting of a single representative agent. If it does matter, then we need a new approach to understand, predict, and control our world.

简·雅各布斯 (Jane Jacobs) 在其杰出著作《城市与国富论》中告诫经济学家们要在这里找到答案：

Jane Jacobs, in her remarkable book Cities and the Wealth of Nations, admonishes economists to get the answer right here:

我们认为粒子物理学家和太空探索者的实验非常昂贵，事实也确实如此。但与银行、行业、政府和国际机构（如世界银行、国际货币基金组织和联合国）投入到宏观经济理论测试中的难以想象的巨额资源相比，这些成本微不足道。从来没有一门科学或所谓的科学，从未得到过如此慷慨的纵容。实验从未留下如此多的破坏、不愉快的意外、破灭的希望和混乱，以至于人们开始认真思考这些破坏是否可以修复；如果可以，肯定不会再有更多相同的破坏。如果我们关注失败告诉我们的现实，失败可以帮助我们走上正轨。但坦率地说，观察现实从来都不是经济发展理论的优势之一。

We think of the experiments of particle physicists and space explorers as being extraordinarily expensive, and so they are. But the costs are as nothing compared with the incomprehensibly huge resources that banks, industries, governments and international institutions like the World Bank, the International Monetary Fund and the United Nations have poured into tests of macro-­economic theory. Never has a science, or supposed science, been so generously indulged. And never have experiments left in their wake more wreckage, unpleasant surprises, blasted hopes and confusion, to the point that the question seriously arises whether the wreckage is reparable; if it is, certainly not with more of the same. Failures can help set us straight if we attend to what they tell us about realities. But observation of realities has never, to put it mildly, been one of the strengths of economic development theory.

以蜜蜂的蜂巢为例。蜂王产下的每一个卵都要经历一个微妙的发育过程，从卵到幼虫再到蛹，最后从蜂巢中孵化出一只完整的蜜蜂。要使这一过程成功，就需要将蜂巢内的温度保持在一个狭窄的范围内（接近 94 华氏度）。当然，蜂巢外的温度变化很大，那么蜜蜂如何才能将内部温度限制在如此小的范围内呢？

Consider a honeybee hive. Every egg laid by the queen goes through a delicate sequence of development from egg to larva to pupa to finally emerging from its honeycomb cell as a fully formed bee. For this sequence to be successful, it requires a narrow range of temperatures to be maintained inside the hive (close to 94 degrees Fahrenheit). Of course, the temperature outside the hive varies wildly, so how can bees keep the inside temperature confined to such a small range?

事实证明，工蜂有两种与温度相关的行为。当工蜂感觉太冷时，它会寻找其他蜜蜂并快速嗡嗡作响翅膀以产生热量。当工蜂感觉太热时，它会远离其他蜜蜂并扇动翅膀形成气流以降温（见图 4.1）。

It turns out that worker bees have two temperature-­related behaviors. When a worker gets too cold, it seeks out other bees and rapidly buzzes its wings to generate heat. When it gets too warm, it moves away from others and fans its wings to form air currents that will cool things down (see Figure 4.1).

蜂巢内的温度取决于工蜂的行为。蜂巢内没有中央指挥中心，只有通过每只蜜蜂的决定和行动才能完成任务。事实证明，一只蜜蜂的温度相关行为是由基因决定的设定点决定的。温度远高于或低于这个设定点会导致蜜蜂分别采取冷却或变暖行为。

The temperature in the hive depends on the actions of its workers. There is no central command center in the hive, and it is only through the decisions and actions of each individual bee that things get done. It turns out that an individual honeybee’s temperature-related behavior is given by a genetically determined set point. Temperatures much above or below this set point cause the bee to undertake cooling or warming behavior, respectively.

图 4.1：工蜂在蜂巢入口处伸展翅膀，形成气流来冷却蜂巢。这种行为是由基因决定的设定点激活的。（照片由 Jacob Peters 提供。）

Figure 4.1: Worker honeybees spread out at the entrance of their hive and fan their wings to create air currents that will cool the hive. This behavior is activated by a genetically determined set point. (Photograph courtesy of Jacob Peters.)

温度控制似乎是一种种群从同质性中受益的情况——大自然会进化出一个代表性代理。悉尼大学的研究人员（参见 Jones 等人的《蜜蜂巢穴体温调节：多样性促进稳定性》，《科学》，2004 年）调查了这个问题，并发现了令人惊讶的结果。

Temperature control seems like a situation in which a population would benefit from homogeneity—in which nature would evolve a representative agent. Researchers at the University of Sydney (see Jones et al., “Honey Bee Nest Thermoregulation: Diversity Promotes Stability,” Science, 2004) investigated this question and found a surprising result.

作为一个思想实验，假设我们观察一个蜂巢，其中每只蜜蜂的基因恒温器都设置为相同的理想温度。你可能会认为，由于所有蜜蜂的基因恒温器都设置为相同的理想温度，蜜蜂的校准非常精确，蜂巢将保持恒定的温度。但事实并非如此。当温度低于设定点时，大量蜜蜂会立即挤在一起，嗡嗡作响翅膀，导致温度大幅上升。随着温度上升，温度很快超过理想点，所有蜜蜂都会切换到冷却行为，四处散开并扇动翅膀，导致温度迅速下降。当温度骤降到理想点以下时，蜜蜂群会再次改变行为。最终出现的不是温度严格控制的蜂巢，而是温度剧烈波动的蜂巢。

As a thought experiment, suppose we observe a hive of bees in which every bee’s genetic thermostat is set to the same ideal temperature. You might think that since all of the bees are so precisely calibrated, the hive will maintain a constant temperature. This is not what happens. When the temperature creeps below the set point, large numbers of bees instantly huddle together and buzz their wings, causing a large increase in the temperature. As the temperature rises, it quickly goes past the ideal point, and all of the bees switch to their cooling behavior and scatter and fan, inducing a rapid drop in temperature. As the temperature plummets below the ideal point, the mass of bees switches behavior yet again. What emerges is not a hive with a tightly controlled temperature but one that experiences wild swings in temperature.

另一种方案是，假设我们有一个由不同种类的蜜蜂组成的蜂巢，每只蜜蜂在理想温度附近都有一个略微不同的设定点。在这个蜂巢中，当温度开始低于理想点时，只有少数蜜蜂开始挤在一起并提供一点额外的温暖，从而慢慢提高温度。事实上，只要温度超过或低于理想点，蜜蜂就会逐渐做出反应，一开始只有少数蜜蜂加入，只有当温度开始偏离理想点时，才会有更多的蜜蜂加入。最终，这种异质策略使蜂巢能够保持精确的温度，只有最小的波动。

As an alternative, suppose that we have a hive of heterogeneous bees, each with a slightly different set point around the ideal temperature. In this hive, as the temperature starts to creep below the ideal point, only a few bees start to huddle together and provide a little additional warmth, slowly raising the temperature. Indeed, any time the temperature overshoots or undershoots the ideal point, there is a graduated response by the bees, with only a few joining in at first, and more joining in only if things start to stray further from the ideal. Ultimately, this heterogeneous strategy allows the hive to maintain a precise temperature with only minimal oscillations.

因此，拥有异质性蜜蜂种群可以适应蜂巢，从而可以更严格地控​​制温度，并提高育雏成功率。在真正的蜂巢中，处女蜂王在最初几天会在飞行中，她会与来自不同蜂巢的大约 8 到 20 只雄蜂（雄性）交配，而不仅仅是一只。一旦蜂王回到蜂巢，她就会产下工蜂，这些工蜂要么是姐妹，要么是同父异母姐妹，从而保证它们之间存在一定的异质性。

Thus, having a heterogeneous population of honeybees is adaptive to the hive, leading to a much more tightly controlled temperature and greater success in brood rearing. In real hives the virgin queen spends her first few days going out on flights where she mates with around eight to twenty drone (male) honeybees from different hives, rather than just one. Once the queen is back in her hive, she produces worker bees that are either sisters or half-sisters to one another, guaranteeing some heterogeneity among them.

在我们的同质和异质蜂巢中，蜜蜂的平均温度设定点是相同的。不同之处在于，在异质蜂巢中，设定点会围绕这个平均值出现一些差异，而在同质蜂巢中，每个工蜂的设定点都相同。因此，至少就蜜蜂蜂巢而言，代表性代理模型会非常具有误导性，它暗示蜂巢温度会剧烈波动，而实际上它们相当稳定。

The average temperature set point of the honeybees was the same in both our homogeneous and heterogeneous hives. The difference was that in the heterogeneous hive there was some variance of the set points around this average, whereas in the homogeneous hive every worker had the same set point. So, at least in terms of a honeybee hive, the representative agent model would be very misleading, implying hive temperatures that oscillate wildly when in fact they are actually quite stable.

现在考虑一个市场模型。假设市场由同质的代表性交易者组成，他们根据收到的信息决定买入或卖出。就像我们在蜜蜂身上看到的那样，这种类型的模型将导致一些不寻常的市场行为。随着市场中的信息开始发生变化，在某个时候，代表性交易者会想要买入。由于所有交易者都使用相同的规则，这将导致需求急剧增加，价格将迅速上涨。随着价格上涨，信息最终会发生变化，所有交易者都想卖出，从而导致价格暴跌。就像蜂巢的情况一样，具有同质交易者的市场会导致价格剧烈波动。

Now consider a model of a market. Let’s assume that the market is populated by homogeneous representative traders who decide to buy or sell based on incoming information. Just as we saw with the honeybees, this type of model is going to result in some unusual market behavior. As the information in the market begins to change, at some point the representative trader is going to want to buy. Since all of the traders use the same rule, this is going to cause a drastic increase in demand, and prices will experience a rapid rise. As prices go up, the information eventually changes to a point where, in perfect synchronicity, all of the traders want to sell, inducing a price crash. As in the case of the hive, a market with homogeneous traders leads to wild price oscillations.

只有当交易者类型多样时，市场才会稳定。交易者类型多样，对信息变化的反应也各有不同，轻微的信息变化只会影响最敏感的交易者，而更极端的变化则会引发不太敏感的交易者的反应。这样的市场会比同质市场表现得更好，价格波动会更温和，价格发现也会更合理。

Stable markets emerge only with heterogeneous agents. With many types of traders, responses to changing information are graduated, with slight changes in information influencing only the most sensitive traders, and more extreme changes provoking responses from the less sensitive traders. Such a market will be much better behaved than a homogeneous one, experiencing milder price swings and more reasonable “price discovery.”

在蜂巢和市场中，异质性提供了所需的稳定性，但在其他系统中并非总是如此。假设我们想要模拟社会运动的动态，从社区层面的骚乱到推翻国家政府。假设我们社会中的一百人中的每一个人都有敏感度S，这样如果她观察到S或更多人参与运动，她就会加入。最后，假设有一群外部煽动者试图发起这场运动。

In hives and markets heterogeneity provides needed stability, but this is not always the case in other systems. Suppose we want to model the dynamics of a social movement, ranging from a neighborhood-level riot to the overthrow of a national government. Let’s assume that each of, say, one hundred people in our society has a sensitivity level, S, such that if she observes S or more people participating in the movement, then she will join. Finally, let’s assume that there is a group of outside rabble-rousers that tries to start the movement.

假设我们这 100 个人的敏感度都设定为 50，那么需要多少个煽动者才能引发一场全面的社会运动？如果煽动者的数量少于 50，那么没有人会加入这场运动。如果煽动者的数量为 50 或以上，那么每个人都会加入。因此，在一个同质世界中，至少需要与固定敏感度一样多的煽动者才能催化一场运动。在这个例子中，我们需要相当多的煽动者——相当于人口的一半——才能看到一场全面的社会运动。

Assume that our one hundred people all have the same sensitivity level set at, say, 50. How many rabble-rousers will it take to trigger an all-out social movement? If the number of rabble-rousers is less than fifty, then no one else joins in the fray. If the number of rabble-rousers is fifty or above, then everyone joins. Thus, in a homogeneous world, it takes at least as many rabble-rousers as the fixed sensitivity level to catalyze a movement. In this example, we need a fairly large number of rabble-rousers—equal to half of the population—before we see a full-blown social movement.

或者，假设我们的人口结构非常复杂，一百个人中每个人都有独特的敏感度。举一个极端的例子，将人口排成一排，给第一个人的敏感度 1，给第二个人的敏感度 2，依此类推，直到最后一个人的敏感度 100。在这个世界上，需要多少个煽动者来催化一场全社会的社会运动？答案当然是一个。一个煽动者就足以让敏感度为 1 的人加入，一旦有两个人加入运动，就足以让敏感度为 2 的人加入，从而引发第三个人（根据 Arlo Guthrie 的歌曲“Alice's Restaurant”，这构成了一个组织），依此类推，直到我们社会的所有一百名成员都加入了这场运动。

Alternatively, assume that we have a very heterogeneous population, with each of our one hundred people having a unique sensitivity. To make this an extreme example, line up the population and give the first person a sensitivity of 1, the second a sensitivity of 2, and so on down the line, until the last person is assigned a sensitivity of 100. In this world, how many rabble-rousers are needed to catalyze a society-wide social movement? The answer, of course, is one. One single rabble-rouser is enough to get the person with a sensitivity of 1 to join in, and once we have two people in the movement, that is enough to get the person with a sensitivity of 2 to join, and this triggers the third (which, according to Arlo Guthrie’s song “Alice’s Restaurant,” constitutes an organization), and so on down the line, until all one hundred members of our society have joined the movement.

上述两个社会世界都有一个临界点，低于这个临界点，没有人会加入运动，高于这个临界点，每个人都会加入运动。当然，这两个世界的临界点截然不同，第一个临界点等于 50 人（人口的一半），第二个临界点只有一个。请注意，在这两个世界中，人口的平均阈值约为 50 人，因此不同的临界点是由于两个世界的阈值不同造成的。在第一个世界中，同质代理的存在意味着没有差异，而在第二个世界中，代理的异质性会引起很大的差异。

Both of the social worlds above are characterized by a critical tipping point, whereby below this point no one joins the movement and above it everyone does. Of course, this tipping point is dramatically different in the two worlds, being equal to fifty (half the population) in the first and only one in the second. Note that in both worlds, the average threshold for the population is about fifty, so the different tipping points are due to the variations in the thresholds of the two worlds. In the first world, the presence of homogeneous agents implies no variance, while in the second agent heterogeneity induces a lot of variance.

因此，在社会运动模型中，我们发现异质性导致不稳定而不是稳定的案例蜜蜂和抗议都具有一些共同的重要特征，这些特征导致了结果的巨大差异。在这两种情况下，异质性都会导致渐进式响应，即环境的细微变化会导致系统行为的细微变化。两种模型之间的区别在于它们产生的反馈类型。在蜂巢温度调节的情况下，系统受负反馈控制，渐进式响应往往会使系统稳定。在社会运动的情况下，存在正反馈，渐进式响应就像滚动的雪球，积雪会使它变得更大更重，并且更有可能积聚更多的雪。

Thus, in the social movement model, we find a case where heterogeneity leads to instability rather than stability. However, both the bees and the protest share important characteristics that underlie the dramatic difference in outcomes. In both cases, heterogeneity leads to a graduated response, where slight changes in the environment cause slight changes in the system’s behavior. The difference between the models is in the type of feedback they engender. In the case of hive temperature regulation, the system is governed by negative feedback, and having a graduated response tends to stabilize the system. In the case of the social movement, there is positive feedback, and a graduated response is like a rolling snowball, where the accumulation of snow makes it bigger and heavier and more likely to pick up additional snow.

尽管反馈类型不同，但这两个模型都对代表性代理提出了相同的基本观点：它们可能具有很大的误导性，因为平均值并不是信息。如果我们考虑所有代理都以平均值行动的系统，我们通常会做出错误的预测，对蜜蜂的情况期望太低，对社会运动的情况期望太高。

Despite the type of feedback in play, both models make the same essential point about representative agents: they can be quite misleading, as the mean is not the message. If we consider systems with all agents acting at the mean, we will often make bad predictions, expecting too little stability in the case of the honeybees and too much in the case of social movements.

政策通常可以影响系统的异质性水平，从而决定系统的整体行为。异质性可能是市场中的一种稳定力量，因此我们可能希望通过确保我们拥有许多中等规模的贸易公司使用专有交易算法相互竞争来鼓励多样性。但是，如果你想要镇压社会叛乱，拥有一个具有高门槛的同质人口将防止小事件发展成革命。虽然政策不能决定同质人口，但它可以通过改变个人收到的有关合理门槛水平或活动家数量的信息来影响反馈回路。或者，如果你想从一个小火花发起一场社会运动，那么你需要鼓励观点的多样性和每个人都参与其中的感觉，这样一粒火花就可以引发连锁反应，点燃一场全面的运动——只需一个环就能把他们全部带走。

Policy can often influence the level of heterogeneity in the system and thus determine the system’s overall behavior. Heterogeneity is likely to be a stabilizing force in markets, and therefore we might want to encourage diversity by ensuring that we have many moderately sized trading houses competing with one another using proprietary trading algorithms. However, if you want to quash a social rebellion, having a homogeneous population with a high threshold will prevent small events from growing into revolutions. While policy can’t dictate a homogeneous population, it can influence the feedback loops by, say, altering the information individuals receive about reasonable threshold levels or the number of activists. Alternatively, if you want to initiate a social movement from a small spark, then you want to encourage a diversity of views and a sense that everyone is participating, so that a single spark can lead to a cascade that ignites a full-blown movement—it takes just one ring to bring them all.

五

five

从六西格玛到新型鸡尾酒：噪音

From Six Sigma to Novel Cocktails: Noise

错误……是发现的门户。

Errors . . . are the portals of discovery.

—詹姆斯·乔伊斯

—James Joyce

年代六西格玛是摩托罗拉公司从 20 世纪 80 年代开始开发的一种业务管理系统。该系统旨在改进制造流程。其核心是一套技术，旨在将流程中的缺陷数量限制在每百万 3.4 个或更少（或者，相当于使 99.99966% 的流程产品无缺陷）。六西格玛理念的应用，以及更广泛地说，通过消除错误来提高质量的概念，可能为从微芯片制造到医疗保健等行业的生产商带来了大量节省，并为消费者带来了更多利益。

Six Sigma is a business management system developed by Motorola starting in the 1980s. It was designed to improve manufacturing processes. At its heart is a set of techniques that attempts to limit the number of defects in a process to 3.4 per million or fewer (or, equivalently, having 99.99966 percent of the products emerging from the process defect free). The application of Six Sigma ideas and, more generally, the notion of improving quality by eliminating errors have likely resulted in substantial savings to producers and increased benefits to consumers in industries ranging from microchip fabrication to health care.

鉴于六西格玛等例子和我们自己的直觉，我们很容易认为消除系统中的错误（通常被归类为“噪音”）将带来更好的结果。制造业在很多方面与新兴系统相反。它是一个依靠同质性蓬勃发展的系统。但是，正如我们在上一章中看到的，有时你需要异质性来驱动一个系统。虽然避免错误对于制造定义明确的商品很有用，但如果我们想发现新事物，这是一种危险的偏见。

Given examples such as Six Sigma and our own intuitions, it is easy to think that eliminating errors in a system—what often gets classified as “noise”—will lead to a better outcome. Manufacturing is in many respects the opposite of an emergent system. It is a system that thrives on homogeneity. But, as we saw in the previous chapter, there are times when you need heterogeneity to drive a system. While error avoidance is useful in the manufacture of a well-defined good, it is a dangerous bias if we want to discover new things.

考虑寻找某个景观中最高海拔的问题。当您踏过景观时，您的纬度和经度会随着每一步而改变，如果景观中有丘陵和山谷，您的海拔也会改变。这种海拔寻找是跨两个维度（纬度和经度）的简单搜索问题（寻找最高海拔）的一个例子。

Consider the problem of finding the highest elevation on some landscape. As you tread across the landscape, you change your latitude and longitude with each step, and if the landscape has hills and dales, you’ll also change your elevation. Such elevation seeking is an example of a simple search problem (searching for the highest elevation) across two dimensions (latitude and longitude).

如果天气晴朗，我们可以乘坐热气球俯瞰大地，或者我们可以快速浏览地形图（由高程等高线组成，像涟漪一样围绕着各个山丘和山谷），那么找到最高海拔就相当容易了。无论从哪种视角，我们都可以快速识别出陆地上的最高点，并找到其相关的经纬度。在这种情况下，无论从哪种视角看世界，消除错误的六西格玛方法都会非常有效。

If the day is clear and we can take a hot-air balloon journey and rise above the landscape, or if we can quickly scan a topographic map (composed of contour lines of elevation spreading out like ripples around various hills and dales), then finding the highest elevation is fairly easy. With either type of view we can quickly identify the highest point in the land and find its associated latitude and longitude. In such a situation, with either view of the world, the error-eliminating Six Sigma approach would work like a charm.

为了让这个场景更具挑战性，假设浓雾弥漫，我们的视野被限制在当前位置周围几英尺内。在这种情况下（这是现实世界中搜索问题的常态），我们该怎么办？

To make this scenario a bit more challenging, suppose a dense fog rolls in, thus limiting our vision to just a few feet surrounding our current position. Under such conditions—which are the norm in real-world search problems—what can we do?

这里一个明显的搜索策略就是环顾我们当前被雾包围的位置，然后向上走一步。一旦我们迈出这一步，我们就可以重新环顾四周，因为一些新的领域将会显露出来，我们可以再次向上走。有时我们环顾四周，可能会发现一切都是相同的海拔，如果是这样，我们可以随意朝一个方向走。如果我们继续遵循这一搜索策略，我们最终会发现自己处在一个点上，当我们在浓雾中环顾四周时，所有方向都指向下坡。在这里，我们记下我们的坐标，并向全世界宣布我们找到了一个高点。这种搜索策略被称为爬山，这并不奇怪。

An obvious search strategy here is to simply look around our current fog-bound location and take a step uphill. Once we take that step, we can look around anew, as a bit of new territory will be revealed, and we can again step uphill. At times we might look around and find that everything is the same elevation, and if so, we can just step in a random direction. As we continue to follow this search strategy, we will eventually find ourselves at a point where, as we look around in the dense fog, all directions lead downhill. Here we note our coordinates and declare to the world that we have found a high point. This type of search strategy is known, not surprisingly, as hill climbing.

爬山有多好？如果我们环顾四周，发现所有道路都通向下坡，那么我们至少可以保证，当雾散去时，我们将到达当地的一个最高点。然而，没有人能保证这个当地最高点也会是全球最高点。因此，虽然我们可能在雾中攀登结束时宣称我们已经找到了世界之巅，但当雾散去时，我们可能会发现自己站在珠穆朗玛峰脚下的蚁丘上。

How well does hill climbing work? If, when we look around, all roads lead downhill, we can at least guarantee that when the fog lifts we will be at a local high point. There is no guarantee, however, that this local high point will also be the global high point. Thus, while we might declare at the end of our fog-bound climbing efforts that we have found the top of the world, when the fog lifts we might find ourselves standing on an anthill at the base of Mount Everest.

爬山搜索的问题在于，我们可能在旅程结束时找到局部最优解，而不是全局最优解。提高找到地形上较高点的几率的方法之一是进行多次爬山，每个人都从不同的随机选择的位置开始。回到我们雾气弥漫的景观，想想随机从几个爬山者身上跳伞，每个人从着陆的地方都遵循爬山算法。如果景观上有很多山丘，那么这些不同的登山者很可能会登上不同的山峰，有些山峰比其他山峰高。因此，有了多个随机的起点，我们很可能会发现新的、更好的最优解。

The problem with a hill-climbing search is that we might end up at a local, rather than global, optimum at the end of our journey. One way to improve our odds of finding the higher points on the landscape is to do multiple hill climbs, each starting from a different, randomly chosen location. Return to our fog-encrusted landscape and think about randomly parachuting down a few hill climbers, each of whom pursues a hill-climbing algorithm from wherever he or she lands. If there are many hills on the landscape, then these different climbers are likely to end up atop different peaks, some higher than others. Thus with multiple, random starting points we are likely to uncover new and better optima.

爬山的有效性与地形的崎岖程度有关。如果地形像富士山周围那样，以对称的火山锥为主，那么无论登山者在哪里着陆，当她上山时，她都会到达山顶并发现自己处于最高点。相反，如果地形类似于喜马拉雅山、安第斯山脉或落基山脉，那么我们的登山者很可能会最终登上当地的山峰，而不是全球的山峰。

The effectiveness of hill climbing is tied to the ruggedness of the landscape. If the landscape looks like that around Mount Fuji, dominated by its symmetrical volcanic cone, then regardless of where a hill climber lands, when she walks uphill she will end up at the peak and find herself at the highest point. If, instead, the landscape resembles that of the Himalayas, Andes, or Rockies, then it will be quite likely that our hill climbers will end up on local rather than global peaks.

考虑图 5.1 所示的一维问题。对于x轴上的任何位置，都有一个由y轴给出的相关海拔。请注意，我们可以取x轴上的任意一点，并计算出从该点出发的登山者爬上山后会到达哪里。或者，我们可以取地形上的任意山峰，并绘制出爬山后到达该山峰的所有x轴值。这样的地图为我们提供了每个局部最优的“吸引盆地”。如果世界就像富士山（想象一个金字塔形状占据整个图表），那么所有x轴的值位于同一个吸引盆地中，而该盆地通向全球最高点。相反，如果世界看起来像图中那样，那么就会有三个盆地，每个盆地都通向不同的高峰，高度也不同。

Consider the one-dimensional problem shown in Figure 5.1. For any location along the x-axis, there is an associated elevation given by the y-axis. Note that we can take any point on the x-axis and figure out where a hill climber who starts from this point will end up after marching uphill. Alternatively, we can take any peak on the landscape and map out all of the x-axis values that will lead, after hill climbing, to it. Such a map gives us the “basin of attraction” for each local optimum. If the world is like Mount Fuji (think of a single pyramidal shape dominating the diagram), then all of the x-axis values are in the same basin of attraction, and that basin leads to the global high point. If, instead, the world looks like that of the figure, then there are three basins, each leading to a different peak with a different height.

图 5.1：一维搜索问题及其相关的吸引盆地（假设采用爬山法）。随着地形变得更加“崎岖”，山峰的数量以及吸引盆地的数量也会增加。

Figure 5.1: A one-dimensional search problem, along with its associated basins of attraction (assuming hill climbing). As the landscape becomes more “rugged,” the number of peaks, and thus the number of basins of attraction, increases.

我们还可以在多维景观中识别出吸引盆地。在我们最初讨论的二维景观中，想象一下一场淹没世界的大洪水。随着水开始蒸发，出现的第一块陆地将是全球高峰。随着水沿着这座山峰的两侧向下流动，相关的吸引盆地就会显露出来。如果景观崎岖不平，在某个时候就会出现另一片陆地从退潮的海水中升起，露出第二高峰，我们就可以开始确定它的吸引盆地了。随着水位进一步下降，浮现出的各个陆地岛屿最终会相互接触，正是在这些点上，我们确定了吸引盆地的边界。如果随着水位的下降，我们有一个陆地点逐渐扩大到覆盖整个世界，那么爬山者将很容易找到全球高峰。相反，如果出现了许多岛屿，那么爬山者很可能会困在较低的山峰上。

One can also identify basins of attraction in landscapes with more than one dimension. In the case of the two-­dimensional landscape we initially discussed, think about a great flood inundating the world. As the waters begin to evaporate, the first bit of land that emerges will be the global peak. As the waters move down the sides of this peak, the associated basin of attraction is revealed. If the landscape is rugged, at some point another island of land will emerge from the receding waters, revealing the second-highest peak, and we can begin to identify its basin of attraction. As the waters fall further, the various islands of land that are emerging will eventually touch one another, and it is at these points that the boundaries of the basins of attraction are identified. If, as the waters recede, we have a single point of land growing to encompass the entire world, then hill climbing will easily find the global peak. If, instead, numerous islands pop up, then hill climbing will likely get trapped on a lower-lying peak.

从上文中我们可以看出，地形的崎岖程度是爬山法能否找到最高点的重要因素。这留下了两个关键问题：什么决定了地形的崎岖程度？当我们面对崎岖地形时，有没有比爬山法更好的搜索方法？

From the above, we see that the ruggedness of the landscape is an important factor in the ability of hill climbing to discover the highest point. This leaves open two key questions: what determines ruggedness, and are there better ways to search than hill climbing when we confront a rugged landscape?

崎岖性问题与我们沿任何方向穿越景观时海拔变化的可预测性有关。如果我们从景观边缘的随机位置开始，选择一个随机方向，然后开始沿直线行走，我们可以跟踪从上升切换到下降的次数，反之亦然。如果这些穿越往往很少有切换，景观就会相对平坦，而如果切换很多，景观就会崎岖不平。当我们的切换很少时，搜索的坐标（维度）相对独立。也就是说，如果沿着我们的穿越，海拔的上升或下降与我们在景观上的位置无关，那么地形就不会崎岖。但是，如果搜索的各个维度开始相互影响（即，如果我在稍微改变经度时所经历的海拔变化与我当前的纬度密切相关），那么地形就会崎岖不平。

The issue of ruggedness is tied to the predictability of elevation changes as we traverse the landscape in any given direction. If we start at a random location on the edge of the landscape, pick a random direction, and start walking in a straight line, we can keep track of the number of times we switch from ascending to descending, and vice versa. Landscapes will be relatively smooth if these traverses tend to have very few switches, and rugged when they have a lot. When we have very few switches, the coordinates (dimensions) of the search are relatively independent of one another. That is, if along our traverse the gains or declines in elevation are not tied to where we are on the landscape, then the landscape will not be rugged. However, if the dimensions of the search start to react with one another—that is, if the elevation change that I experience when I change my longitude by a little is closely tied to my current latitude—then the landscape will be rugged.

各个维度之间有大量相互作用的系统被称为非线性系统。奇怪的是，科学界有一个专门研究非线性系统的领域。这很奇怪，因为几乎所有现实世界的系统都存在一定程度的非线性，所以科学将世界的一个方面视为某种杂耍般的好奇心，而这实际上是常态。数学家斯坦·乌拉姆（Stan Ulam）的一句话概括了这一观察：“使用非线性科学这样的术语就像将动物学的大部分内容称为对大象以外的动物的研究。”

Systems that have a lot of interaction among their various dimensions are known as nonlinear systems. Oddly, there is a specialized area of science devoted to the study of nonlinear systems. The reason this is odd is that some degree of nonlinearity is present in almost all real-world systems, so science treats as some sideshow curiosity an aspect of the world that is actually the norm. This observation was captured in a remark apparently made by the mathematician Stan Ulam: “Using a term like nonlinear science is like referring to the bulk of zoology as the study of non-­elephant animals.”

如果我们考虑的搜索问题不仅仅是在物理景观中找到最高点，那么维度和坚固性之间的相互作用概念就会变得更加有趣。例如，想象一下尝试穿得时髦。这里可能涉及的一些维度可能是服装的款式、颜色、腰带的选择、鞋子的类型等等。如果这些维度不相互作用，那么穿着时髦的衣服出门就相对容易了。首先，你要从众多的腰带中找到最好的一条。然后，你挑选最时髦的鞋子。接下来，选择最好的颜色。如此反复，直到你穿着理想的搭配出门。

The notion of interacting dimensions and ruggedness gets far more interesting if we consider search problems other than finding the highest point on a physical landscape. For example, think about trying to dress in a fashionable way. Some of the potential dimensions here might be the style of the outfit, its color, choice of belt, type of shoe, and so on. If these dimensions don’t interact, then leaving the house in a fashionable outfit is relatively easy. First you find the best belt among the lot. Then you pick the most fashionable shoes. Next, pick the best color. And on and on, until you leave the house dressed in the ideal combination.

当然，在时尚界，就像在生活中一样，不同的维度确实会相互影响。鞋子的选择取决于衣服的颜色和类型，腰带需要与鞋子相配（我经常被告知），等等。因此，只优化每个维度而忽略其他维度可能会导致整体搭配成为时尚败笔。此外，可能有许多不同的搭配可以很好地搭配在一起，每种搭配都代表着局部最优（风格），无法通过对任何一个元素进行微小更改来改进。也许其中一种搭配比其他所有搭配都更好，我们可以找到时尚前卫思维的终极体现，尽管这些截然不同的搭配更有可能以大致相同的成功率解决时尚外观问题。

Of course, in fashion, as in life, different dimensions do interact quite a bit. The choice of shoes depends on the color and type of outfit, the belt needs to be coordinated with the shoes (or so I’m often told), and so on. Thus, optimizing on each dimension alone and ignoring the others is likely to lead to an overall ensemble that is a fashion faux pas. Moreover, there are likely to be many different ensembles that work well together, each representing a local optimum (style) that cannot be improved upon by making minor changes in any one element. Perhaps one of these ensembles is better than all of the others, and we can find the ultimate in fashion-forward thinking, though more likely than not these radically different ensembles may each solve the problem of looking fashionable with roughly equal success.

许多其他选择往往具有崎岖不平的地形特征。考虑寻找汽车的最佳设计。汽车的各种特征，例如车门数量、尾翼的存在与否、发动机大小、硬顶或软顶、轴距、重量、行驶里程等，都以令人惊讶的方式相互作用，因此汽车设计的空间可能非常崎岖。在这样的地形中，法拉利 250 GTO、丰田卡罗拉和福特 F150 都可能成为汽车设计问题的局部最优解。同样，考虑寻找最佳鸡尾酒的问题，无论是混合饮料还是药物。如果鸡尾酒的各种元素不相互作用，那么我们只能一次优化一个元素寻找最理想的鸡尾酒，然后通过这种搜索将所有理想点结合起来，调制出最完美的鸡尾酒。当然，这种方法往往会导致鸡尾酒在混合饮料中相当不开胃（曼哈顿冰茶可能是一个罕见的反例），在药物中无效且（可能）危险。

A lot of other choices tend to be characterized by rugged landscapes. Consider finding the best design for a car. The various features of a car, such as the number of doors, presence or absence of tail fins, size of the engine, hard or rag top, wheelbase, weight, mileage, and so on, all interact with one another in surprising ways, and thus the space of car designs is likely to be very rugged. Out of such a landscape, a Ferrari 250 GTO, a Toyota Corolla, and a Ford F150 might all emerge as locally optimal solutions to the problem of car design. Similarly, consider the problem of finding the best cocktail, in either the mixed-drink or drug sense. If the various elements of the cocktail do not interact, then we can just optimize on one element at a time, find its ideal, and from such a search combine all of the ideal points to make the ultimate cocktail. Of course, such an approach tends to result in cocktails that are fairly unappetizing in the case of mixed drinks (with perhaps a rare counterexample given by the Manhattan iced tea) and ineffective and (likely) dangerous in the case of drugs.

虽然爬山可以让我们开着吉普车和登山靴去探索峡谷地国家公园，或者开着宾利和燕尾服去参加正式活动，但它也有可能让我们被困在不那么理想的山峰上。在崎岖的地形上摆脱爬山陷阱的一种方法是将噪音或错误引入搜索算法。我们上面勇敢的爬山者遵循六西格玛的口号，总是朝着没有错误的可能性的山上前进。然而，对改进制造过程有益的东西可能对发现不利。

While hill climbing could lead us to a Jeep and a pair of hiking boots to explore Canyonlands National Park and a Bentley and a tuxedo for a formal, it has the potential to leave us trapped on much less desirable peaks. One escape from the traps of hill climbing on a rugged landscape is to introduce noise or error into the search algorithm. Our intrepid hill climbers above followed the Six Sigma mantra and always headed uphill without the possibility of error. However, what’s good for refining a manufacturing process is likely bad for discovery.

回到我们这位雾蒙蒙、寻求海拔的徒步旅行者，她站在珠穆朗玛峰脚下的蚁丘上。当她从现在的位置环顾四周时，她只看到下山的机会。如果她要逃离土丘并爬上珠穆朗玛峰，她必须采取一些下坡措施。这意味着她需要在爬山搜索中犯一个错误，并至少向下走一步。虽然这似乎与她找到尽可能高点的总体目标相矛盾，但这种短期损失提供了长期潜力，使她能够转移到一个新的斜坡上，这可能会让她发现一个更高的山峰。

Return to our fog-bound, elevation-seeking hiker who is standing on an anthill at the base of Mount Everest. When she looks around from her current perch, she sees only opportunities to descend. If she is to escape the mound and climb Everest, she must take some downhill steps. This implies that she will need to make an error in her hill-climbing search and take at least one step downhill. While this is seemingly at odds with her overall goal of finding the highest point possible, this short-term loss offers the long-term potential of moving her to a new slope that might result in her discovering a much higher peak.

一种采用这种误差爬山法的搜索算法被称为模拟退火。在实际退火中，通过加热物体然后让其缓慢冷却来改善玻璃或金属等材料的特性。在此类材料中，在其他条件相同的情况下，单个原子倾向于彼此对齐。当加热时，这种趋势会被外部能量引入的噪声所淹没，原子会向各个方向摆动。如​​果加热的材料快速冷却，原子会冻结在淬火时它们所面对的任何混乱方向。然而，如果材料冷却得非常慢，随着温度降低，原子的摆动慢慢减弱，它们彼此对齐的愿望开始占上风。最终，材料冷却到大多数原子对齐的状态。这种晶体结构通常会使所得材料具有理想的特性。

A search algorithm that embraces this hill-climbing-with-error idea is known as simulated annealing. In real annealing, the properties of a material such as glass or metal are improved by heating the object and then allowing it to cool slowly. Within such materials, the individual atoms have a tendency to align with one another, all else being equal. When heated, this tendency gets overwhelmed by the noise introduced by the outside energy, and the atoms flop about in all directions. If the heated material is quickly cooled, the atoms get frozen in whatever scrambled directions they were facing at the time of the quenching. However, if the material is cooled very slowly, as the flopping about of the atoms slowly diminishes with the lowering temperature, their desire to align with one another begins to take over. Eventually the material cools to a state in which most of the atoms are aligned. Such crystalline structures often give the resulting material desirable properties.

模拟退火使用与实际退火非常相似的思想。我们采用标准的爬山算法，该算法具有理想的上坡趋势，并通过高“温度”对其施加一些噪音。虽然算法仍然想要上坡，但只要温度高或海拔损失很小，噪音就会使其愿意接受偶尔的错误并下坡。随着时间的推移，我们降低温度，减少算法采取大步下坡的趋势，直到温度低到算法恢复到纯爬山行为。

Simulated annealing uses an idea very similar to that of real annealing. We take our standard hill-climbing algorithm, with its desirable tendency to march uphill, and impose on it some noise via a high “temperature.” While the algorithm still wants to march uphill, the noise makes it willing to accept occasional errors and march downhill as long as the temperature is high or the loss of elevation is small. Over time, we reduce the temperature, lessening the algorithm’s tendency to take large downhill steps, until the temperature is so low that the algorithm reverts to its pure hill-climbing behavior.

在搜索过程中故意引入此类误差使我们能够克服崎岖地形的常见陷阱（见图 5.2）。本质上，我们引入的噪音开始震动地形，填满小山谷，使搜索者能够穿越这些以前无法逾越的障碍，前往更高的地方。噪音让徒步旅行者能够走出蚁丘，继续攀登珠穆朗玛峰。与大多数事情一样，这里也有权衡。噪音的增加，至少在短期内，往往会降低性能，并且在富士山等容易逾越的地形上，它会增加搜索时间，因为方向正确的上坡步骤有时会被下坡步骤抵消。当然，噪音的好处是，在更崎岖的地形上，它总体而言，其性能表现要好得多，因为它允许登山者摆脱低洼的局部最优。

The intentional introduction of such errors into the search process gives us the ability to overcome the usual traps of rugged landscapes (see Figure 5.2). In essence, the noise we introduce begins to vibrate the landscape, filling in the small valleys enough so that the searcher can traverse these previously insurmountable obstacles on her way to higher ground. Noise allows the hiker to step off the anthill and proceed up Everest. There is, as in most things, a trade-off here. The addition of noise, at least in the short term, tends to lessen performance, and on easily surmounted landscapes such as Mount Fuji, it adds additional time to the search, as well-directed uphill steps are occasionally counteracted by downward ones. Of course, the benefit of noise is that on more rugged landscapes it results in much better performance overall, as it allows the climbers to escape low-lying local optima.

图 5.2：模拟退火引入的偶尔下坡步骤允许徒步旅行者逃离较差的局部最优解并最终发现全局最优解。

Figure 5.2: The occasional downhill steps introduced by simulated annealing allow the hiker to escape inferior local optima and ultimately discover the global optimum.

上述想法的一个绝佳应用就是解决发现新型有效的化疗药物组合的问题。多年来，药物发现的形式多种多样。有时药物是从民间偏方中分离出来的，例如从柳树皮中分离出阿司匹林。有时，我们通过收集各种植物、动物和微生物的化合物，然后筛选这些化合物来对抗各种疾病，以期找到有效的药物，例如产生青霉素的真菌。最近，我们尝试直接设计药物，首先确定疾病中潜在的分子弱点，然后设计适当的药物来攻击这种弱点——这通常归结为确定利用弱点所需的蛋白质形状，然后利用有关各种分子组合如何折叠成三维物体的知识来生成该形状。

A nice application of the above ideas is to the problem of discovering novel and effective cocktails of drugs for chemotherapy. Drug discovery has taken many forms over the years. Sometimes drugs were isolated from folk remedies, such as the bark of the willow tree, which gave us aspirin. At other times we found new drugs by collecting chemical compounds from various plants, animals, and microbes and then screening these compounds against various diseases in the hope of finding something that works, such as the fungus that resulted in penicillin. More recently we have tried to design drugs directly, by first identifying a potential molecular weakness in a disease and then designing an appropriate drug to attack this vulnerability—this typically comes down to identifying the shape of a protein needed to exploit the weakness, and then generating that shape using knowledge about how various combinations of molecules fold into three-dimensional objects.

所有这些方法都产生了有用的药物，尽管有时价格昂贵。不幸的是，希望找到一种药物来治愈每种疾病的前提是该疾病有一个致命弱点，可以用巴黎之箭的化学等价物来攻击。然而，大多数疾病存在于复杂的生物系统领域，这样的系统往往具有内置的冗余，使整个系统在面对单一攻击时保持稳健。虽然这样的系统不会屈服于单一攻击，但它们容易受到一连串箭的攻击，每支箭都瞄准不同的目标，总体目标是同时中和足够多的冗余，使整个系统失效。这种复杂系统疾病观表明，如果我们要治愈疾病，可能需要药物鸡尾酒，每种药物都像上述齐射中的一支箭一样发挥作用。

All of these approaches have resulted in useful, albeit at times expensive, drugs. Unfortunately, the hope of finding a single drug to cure each disease assumes that the disease has an Achilles’ heel that can be attacked by the chemical equivalent of the arrow of Paris. However, most diseases exist in the realm of complex biological systems, and such systems tend to have built-in redundancies that make the system as a whole robust in the face of a single line of ­attack. While such systems will not succumb to a single ­attack, they are vulnerable to a salvo of arrows each destined for a different target, with the overall goal of simultaneously neutralizing enough of the redundancies so that the system as a whole will fail. This complex-systems view of disease suggests that drug cocktails, with each drug acting like an arrow in the aforementioned salvo, may be needed if we are to cure what ails us.

最著名的药物鸡尾酒疗法或许是用于治疗艾滋病毒/艾滋病的抗逆转录病毒药物。人类免疫缺陷病毒会快速发生变异，因此，虽然只针对病毒的一部分会取得一些短期成功，但这种策略最终会失败，因为会出现绕过最初目标的变异。然而，通过同时使用几种药物攻击病毒——每种药物都针对病毒传播的不同方面，例如病毒代码的转录或组装——能够绕过一种药物的单一变异仍然会被其他药物的攻击所击败，而且没有一种变异能够获得足够的立足点，让病毒群体得以生存。用景观语言来说，这些药物以非线性的方式相互作用。每种药物可能单独失效，但所有药物的鸡尾酒疗法可以战胜疾病。

Perhaps the best-known drug cocktail is the set of antiretroviral drugs used in the treatment of HIV/AIDS. The human immunodeficiency virus undergoes rapid mutation, and so while targeting only one part of the virus will provide some short-term success, this strategy will ultimately fail, as mutations will arise that circumvent the initial target. However, by attacking the virus with several drugs at the same time—each focused on a different aspect of how the virus propagates, such as the transcription of the viral code or its assembly—single mutations capable of circumventing one drug are nevertheless overwhelmed by the attacks of the other drugs, and no single mutation can ever gain enough of a foothold to allow the viral population to survive. In the language of landscapes, these drugs interact in a nonlinear way with one another. Each drug may fail on its own, but a cocktail of all of the drugs defeats the disease.

HIV/AIDS 鸡尾酒疗法是现代科学的胜利。了解突变的作用和驱动该疾病的各种分子机制需要数千名研究人员付出巨大的努力。一旦有了这种理解，同时使用多种药物（每种药物可对抗不同类别的病毒突变）的策略成为一种显而易见的方法。

The HIV/AIDS cocktail is a triumph of modern science. Understanding the role of mutation and the various molecular mechanisms driving the disease required the costly efforts of thousands of researchers. Once this understanding arose, the strategy of simultaneously using multiple drugs, each of which defeated a different class of viral mutations, became an obvious approach.

虽然基于对疾病潜在分子原理的深入了解来开发治疗方法是可取的，但获取此类知识的成本往往非常高昂。这种成本限制了通过这种方式开发的药物和药物鸡尾酒的数量。偶尔，新的治疗方法会偶然出现。例如，用于治疗霍奇金淋巴瘤的药物鸡尾酒就是一位叛逆医生在绝望的病人身上做实验时凭猜测发现的。不过，如上所述，有充分的理由认为药物鸡尾酒可能是一种很好的、​​甚至是必要的治疗疾病的方法。此外，我们已经拥有大量的化学化合物——无论是偶然发现的、辛勤工作的还是两者兼而有之——可用于药物鸡尾酒。因此，我们应该处于一个很好的位置来开发新的、基于鸡尾酒的疾病治疗方法。当然，实施这一科学计划的困难在于，药物之间经常以令人惊讶的方式相互作用，因此我们面临着一个非线性的局面，简单的方法，如将那些单独效果很好的药物制成鸡尾酒，很可能会失败。幸运的是，我们知道如何搜索崎岖的地形，这为解决这个难题提供了潜在的方法。

While developing treatments based on a deep understanding of the underlying molecular principles involved in a disease is desirable, such knowledge tends to be extremely costly to acquire. This cost restricts the number of drugs and drug cocktails that can be developed via this route. Occasionally new therapies arise by accident. For example, the drug cocktail used to treat Hodgkin’s lymphoma was discovered by guesswork on the part of a rebel doctor who experimented on desperate patients. Still, as noted above, there are sound reasons to think that drug cocktails might be a good, and perhaps even necessary, way to treat disease. Moreover, we already have a vast collection of chemical compounds—discovered by serendipity, hard work, or both—available for inclusion in drug cocktails. Thus we should be in a great position to develop new, cocktail-based approaches to curing disease. Of course, the difficulty with pursuing this scientific program is that drugs often interact with one another in surprising ways, and therefore we face a nonlinear landscape in which simple methods, like forming cocktails from those drugs that work well individually, are likely to fail. Fortunately, our knowledge of how to search rugged landscapes provides a potential way out of this conundrum.

与 MD 安德森癌症中心的医生 Ralph Zinner 及其一些同事合作，我一直在使用各种受复杂系统启发的搜索算法来寻找新颖有效的化疗鸡尾酒疗法。我们的第一个测试涉及一组 19 种治疗药物，这些药物是我们从其他研究人员那里讨要、借用和挪用的。对于每种药物，我们首先确定通常可以杀死 10% 特定肺癌细胞株的剂量，我们将这些细胞培养在塑料板中，板上有 96 个孔，每个孔大约有铅笔橡皮擦大小。你可以从 19 种药物中形成超过 50 万 (2 19 ) 种独特的鸡尾酒疗法，每种药物都以固定剂量使用。不幸的是，即使我们的实验室技术员和关键合作伙伴 Brittany Barrett 付出了巨大的努力，由于必须培养各种细胞系、混合药物、孵育细胞并测定结果，我们每周也只能测试大约 20 种鸡尾酒疗法。

In collaboration with Ralph Zinner, a medical doctor at MD Anderson Cancer Center, and some of his colleagues, I have been using various search algorithms inspired by complex systems to find novel and effective chemotherapy cocktails. Our first test involved a set of nineteen therapeutic drugs that we were able to beg, borrow, and appropriate from fellow researchers. For each drug, we first found the dose that would typically kill off 10 percent of a particular strain of lung cancer cells, which we grew in plastic plates dotted by ninety-six wells, each roughly the size of a pencil eraser. There are more than half a million (219) unique cocktails that you can form from nineteen drugs each used at a fixed dose. Unfortunately, even with the heroic efforts of our laboratory technician and key collaborator, Brittany Barrett, we could test only about twenty cocktails every week, given the constraints of having to grow the various cell lines, mix the drugs, incubate the cells, and assay the outcomes.

为了克服这些限制，我们引入了一种搜索算法，类似于之前描述的爬山算法。我们从 20 种随机配制的鸡尾酒开始。每种鸡尾酒都被添加到几个培养癌细胞的孔中，几天后我们进行了一次分析，看看有多少癌细胞存活下来。杀死更多癌细胞或使用更少药物的鸡尾酒（隐含的权衡是，如果一种药物杀死的癌细胞至少多 10%，则将其加入混合物中）被判定为更适应，这一衡量标准类似于我们徒步旅行者的海拔高度。我们从最初的 20 种鸡尾酒中选出最适合的鸡尾酒，并将其作为我们的现状。然后我们开始爬山。对于每一步，我们都查看了与原始鸡尾酒相同的 19 种药物鸡尾酒除了包括一种不属于现状的药物或排除一种属于现状的药物外，其余的药物都与现状保持一致。然后，我们根据现状测试了这 19 种变体。如果这些变体中适应度最高的一种比现状更好，我们就将这种混合物作为新的现状，并继续搜索。另一方面，如果在查看所有变体时发现现状仍然是最适合的，那么搜索就结束了，因为我们找到了一个局部峰值。

To overcome these limitations, we introduced a search algorithm much like the hill climber described previously. We started with twenty randomly formulated cocktails. Each cocktail was added to a few wells growing the cancer cells, and after a few days we did an assay to see how many of the cancer cells survived. Cocktails that killed more cancer cells or used fewer drugs (with an implicit trade-off of including a drug in the mix if it killed at least 10 percent more of the cancer cells) were judged to have more fitness, a measure akin to our hiker’s elevation. We took the fittest cocktail out of the initial twenty and made that our status quo. Then we started to hill climb. For each step, we looked at the nineteen drug cocktails that were identical to the ­status quo except for either including one drug that was not in the status quo or excluding one that was. Then we tested these nineteen variations against the status quo. If the fittest one of these variations was better than the status quo, we made that cocktail the new status quo and continued our search. If, on the other hand, when we looked at all of the variants we found that the status quo was still the fittest, the search was over, as we had found a local peak.

大约九步之内，我们从 524,288 种可能的鸡尾酒中调查了几百种，我们发现了一种三药鸡尾酒，其适应度比我们随机生成鸡尾酒的预期高出四个标准差。此外，在发现这种三药鸡尾酒后，我们进行了文献检索，发现其中两种药物之前曾被认为可用于另一种癌症的化疗鸡尾酒。我们鸡尾酒中的第三种药物不是我们预期看到的，因为它单独使用时往往会增加癌症的生长。然而，事后看来，加入它可能有充分的理由。例如，其他两种药物在细胞分裂期间可能特别有效。如果是这样，那么将一种促进分裂的药物与其他两种药物结合使用可能是件好事。

Within about nine steps, in which we investigated a couple of hundred cocktails out of the 524,288 possible ones, we found a three-drug cocktail that had a fitness more than four standard deviations above what we would have expected if we generated cocktails at random. Moreover, after discovering this three-drug cocktail, we did a literature search and found that two of the drugs had previously been suggested as being useful in a chemotherapy cocktail for another type of cancer. The third drug in our cocktail was not one we had expected to see, insofar as it tended to increase the growth of the cancer when used alone. However, in hindsight, there might be good reasons for including it. For example, the other two drugs might be particularly effective during cell division. If so, a drug promoting division might be a good thing to have in combination with the other two drugs.

这项研究只是证明了一个原理。它表明，在崎岖地形上使用搜索概念可能是发现新颖有效的化疗组合的有效方法。

This work was merely proof of a principle. It suggests that using the concepts of search on a rugged landscape may be a useful way to discover novel and effective chemotherapy cocktails.

总体而言，发现有效的药物鸡尾酒疗法面临两大严峻挑战。首先，药物之间的非线性相互作用使得简单的搜索策略（例如将最佳的单个药物组合在一起）变得无效。其次，我们面临着可能鸡尾酒疗法的组合爆炸——也就是说，每次我们添加一种药物（即使是固定剂量），我们就可以测试的可能鸡尾酒疗法的数量就会翻倍（即所有之前添加和不添加新药物的鸡尾酒疗法）。例如，如果有 20 种药物，我们就有超过一百万种可能的鸡尾酒疗法；如果有 21 种药物，我们就有两百万种可能的鸡尾酒疗法；如果有 40 种药物，我们就有一百万种可能的鸡尾酒疗法，以此类推。考虑到这种组合爆炸，即使考虑到现代机器人实验室的进步，我们也无法生成和测试所有可能的鸡尾酒疗法。大多数研究都通过专注于只有几种药物的鸡尾酒疗法来避免组合爆炸——如果有 20 种药物，我们就有超过一百万种可能的鸡尾酒疗法，但只有 190 种双药鸡尾酒疗法（如果我们忽略这两种药物的顺序）。幸运的是，来自复杂系统研究的搜索算法为这两个挑战提供了可能的解决方案，因为它们旨在仅使用有限数量的实验在非线性景观上找到好的解决方案。

In general, there are two serious challenges to discovering effective drug cocktails. First, nonlinear interactions among the drugs make simple search strategies, such as combining the best individual drugs, ineffective. Second, we face a combinatorial explosion of possible cocktails—that is, every time we add a drug (even at a fixed dose), we double the number of possible cocktails that we could test (namely, all of the previous cocktails with and without the new addition). With twenty drugs, for example, we have more than a million possible cocktails, with twenty-one drugs we have two million, with forty drugs we have a million million, and so on. Given this combinatorial explosion, we cannot feasibly generate and test all possible cocktails, even given modern advances in robotic laboratories. Most research gets around the combinatorial explosion by focusing on cocktails with only a couple of drugs—with twenty drugs, there are more than a million possible cocktails, but there are only 190 two-drug cocktails (if we ignore the ordering of the two drugs). Fortunately, search algorithms arising from the study of complex systems offer a possible solution to both of these challenges, as they are designed to find good solutions on nonlinear landscapes using only a limited number of experiments.

在许多方面，上述定向发现药物鸡尾酒研究与医学领域的各种趋势背道而驰。最近，许多化疗研究都集中在针对已知分子机制的药物上。虽然这是一种有用的方法，但揭示潜在机制并设计合适药物所需的努力却令人望而生畏。定向发现几乎采取了相反的方法，有时甚至命令实验室工作人员犯错误。在新墨西哥州圣达菲运行的算法，在不了解医学或生物学的情况下，获取一组符号并根据从休斯顿实验室收到的反馈对其进行操作（熟练的技术人员根据从算法收到的符号混合适当的鸡尾酒，将它们添加到活细胞孔中，经过几天的孵育后向算法报告每个孔中有多少细胞死亡）。虽然这种盲目搜索似乎有些极端，尤其是与分子研究人员密集、聪明和专注的工作相比，但最终我们真正关心的是找到有用的鸡尾酒，无论它们是如何发现的。

In many ways, the directed-discovery drug cocktail research above goes against various trends in medicine. A lot of recent work in chemotherapy has focused on drugs that target well-understood molecular mechanisms. While this is a useful approach, the effort it requires to uncover the underlying mechanism and design an appropriate drug is daunting. Directed discovery takes almost the opposite approach, even at times ordering the lab worker to make mistakes. An algorithm running in Santa Fe, New Mexico, with no knowledge of medicine or biology, takes a set of symbols and manipulates these based on feedback received from a laboratory in Houston (where a skilled technician mixes up the appropriate cocktails given the symbols she receives from the algorithm, adds them to a well of living cells, and after a few days of incubation reports back to the algorithm how many cells died in each well). While such a blind search may seem to be extreme, especially compared to the intensive, intelligent, and dedicated work of molecular researchers, ultimately what we really care about is finding useful cocktails, however they are discovered.

定向发现法寻找鸡尾酒药物，它介于叛逆医生的直觉和获取深层分子知识或大规模筛选天然化合物所需的资源密集型努力之间，处于一个有趣的中间地带。此外，如果定向发现成功，那么了解哪些鸡尾酒药物有效可能会为疾病的潜在分子机制提供新的见解。

The directed-discovery approach to finding drug cocktails inhabits an interesting middle ground between intuitive leaps on the part of renegade doctors and the resource-intensive efforts needed to acquire deep molecular knowledge or to conduct large-scale screenings of natural compounds. Moreover, if directed discovery is successful, having information about what cocktails are effective may provide new insights into the underlying molecular mechanisms of the disease.

尽管开发鸡尾酒疗法具有良好的生物学和复杂系统基础，但存在各种制度、法律和监管限制，这些限制有利于单一药物。例如，制药公司喜欢专注于其努力发现（并申请专利）一种单一的、易于销售的畅销药物，而不是寻找可能涉及其他公司药物或可能有许多替代品的成分药物的鸡尾酒疗法。甚至政府法规也倾向于偏向单一药物。例如，食品和药物管理局目前要求鸡尾酒疗法作为鸡尾酒疗法进行测试和批准——这是一个极其昂贵的过程——即使组成鸡尾酒疗法的药物都是单独批准的。最近，这些机构采取了一些有希望的行动，认识到鸡尾酒疗法的价值并鼓励使用它们。

Notwithstanding the sound biological and complex-­systems basis for pursuing drug cocktails, there are various institutional, legal, and regulatory constraints that favor single drugs. For example, drug companies like to focus their efforts on discovering (and patenting) a single, easily marketable, blockbuster drug, rather than seeking out cocktails that might involve drugs from other companies or component drugs that may have many substitutes. Even government regulations tend to favor single drugs. For example, the Food and Drug Administration currently requires that cocktails be tested and approved as a cocktail—an extremely costly process—even when the drugs that make up the cocktail are all individually approved. Recently there has been some promising movement on the part of such agencies to recognize the value of cocktails and encourage their use.

未来十年，我们很可能进入个性化医疗的新时代。例如，目前的癌症治疗往往粗略地将癌症类型划分为过于宽泛的类别，并将同一类别中的每个人视为患有同一种疾病。医生们对他们进行一般的治疗方案，希望某种疗法能奏效。人们对同一种治疗的反应截然不同，这一事实表明，癌症的个体特异性要高得多。例如，我们知道黑色素瘤有各种类型的突变，使其对不同药物的敏感性或高或低。有充分的理由认为，随着进一步的研究和信息，我们将发现许多这样的特异性。随着我们进入廉价基因分型时代，未来的癌症诊断很可能与个人癌症的基因型有关。一旦发生这种情况，我们可能会进入一个每个病人都患有一种“孤儿”疾病，只有少数人患有这种疾病。在这样的世界里，我们需要一种方法来快速定制每个病人的治疗方案。定向发现可能会成为未来的关键技术。

Over the coming decade we are likely to enter a new era of personalized medicine. For example, current cancer treatments tend to crudely classify types of cancers into overly broad categories and treat everyone within a category as if they shared the identical disease. Doctors run them through general protocols of treatment in the hope that something will work. The fact that people respond quite differently to the same treatment suggests that cancer is far more individually specific. For example, we know that there are various types of mutations in melanoma that make it more or less susceptible to different drugs. There is good reason to think that with further investigation and information, we will uncover many such specificities. As we enter an era of cheap genotyping, it is likely that future cancer diagnoses will be tied to the genotype of an individual’s cancer. Once this occurs, we may enter a world in which each patient has what is essentially an “orphan” disease, shared with only a few others. In such a world we will need a way to quickly customize each patient’s treatment. Directed discovery may prove to be a key enabling technology in such a future.

归根结底，使用鸡尾酒疗法治疗复杂疾病的想法是正确的，鉴于这种搜索所依赖的地形天生崎岖，以及组合爆炸式增长，我们需要一种系统化的方法来发现这种鸡尾酒疗法。世界上有成千上万种化合物可用于构建药物鸡尾酒疗法，其中许多化合物价格低廉，因为它们的专利已经过期。这个蕴含化学知识的宝库，加上机器人技术和微流体技术的新发展，将我们置于一个新时代的开端，在这个时代，针对每位患者个性化的新型有效药物鸡尾酒疗法正在等待被发现——如果我们愿意犯一些错误，与六西格玛相反。

Ultimately, the notion of using cocktails to treat complex diseases is sound, and we need a systematic way to discover such cocktails given the innately rugged landscapes and combinatorial explosion underlying such searches. There are thousands of chemical compounds in the world that could be used to construct drug cocktails, and many of those compounds are quite inexpensive because their governing patents have expired. This storehouse of embodied chemical knowledge, linked with new developments in robotics and microfluidics, places us on the cusp of an era in which novel and effective drug cocktails, personalized to each patient, are waiting to be discovered—if, contrary to Six Sigma, we are willing to make some errors.

六

six

从稻草人到黏菌：分子智能

From Scarecrows to Slime Molds: Molecular Intelligence

如果你脑袋里有脑子，你就会和他们一样优秀，甚至比他们中的一些人更优秀。无论是乌鸦还是人，脑子是这个世界上唯一值得拥有的东西。

If you only had brains in your head you would be as good a man as any of them, and a better man than some of them. Brains are the only things worth having in this world, no matter whether one is a crow or a man.

—L.弗兰克·鲍姆， 《绿野仙踪》

—L. Frank Baum, The Wonderful Wizard of Oz

乙雨水被高估了，通常是那些拥有雨水的人。想想（我们并没有说大脑没用，只是被高估了）世界上所有必须在没有神经元的情况下做出正确决定的实体。举一个例子，每个中性粒细胞（一种白细胞，你可能遇到过细菌（例如从伤口流出的脓液）能够根据化学信号移动到感染部位。到达感染部位后，细菌可以识别外来微生物，并通过吞噬或释放抗菌化学物质来消灭它们。这种复杂的行为在我们世界的每一个角落都比比皆是。而且，这种行为不需要神经元或大脑就能发生。

Brains are overrated, generally by those who have them. Think (we didn’t say brains weren’t useful, they’re just overrated) about all of the entities in the world that have to make good decisions with nary a neuron to be had. To take one example, each neutrophil granulocyte (a type of white blood cell, which you may have encountered in the form of pus emerging from a wound) in your body is capable of moving to sites of infection based on chemical signals. Once there, it can identify foreign microbes and destroy them by ingesting them or releasing antimicrobial chemicals. Such complex behavior abounds in every corner of our world. And it happens without neurons or a brain.

从某种程度上来说，没有神经元的选择并不那么令人惊讶。即使是无生命的东西，比如一滴水或一块滚石，也必须决定去哪里，因为它们会规划出通往地势低点的路线，而且它们以（至少表面上）聪明的方式做到这一点。事实上，无数的计算机时间都花在解决类似类型的问题上，比如我们试图找到送货卡车要走的最短路线。当然，在水和石头的情况下，有一种外力，即重力，推动着解决方案的产生——尽管我们的大脑很聪明，但我们自己很难找到解决方案。

At one level, choice without neurons is not all that surprising. Even inanimate things, such as a drop of water or a rolling stone, have to decide where to go as they map out routes to low points in the landscape, and they do so in (at least ostensibly) clever ways. Indeed, countless computer hours are devoted to solving similar types of problems as we, say, try to find the shortest route for delivery trucks to follow. Of course, in the case of water and stones there is an external force, gravity, that drives the solutions—solutions that, despite our clever brains, we struggle to discover ourselves.

因此，水和石头提供了一个存在性证据，证明聪明并不局限于聪明的事物。然而，当我们观察生物时，这个问题就变得更加有趣了，它们在更接近我们所珍视的领域做出选择。

Water and stones, then, provide an existence proof that cleverness is not restricted to smart things. Yet the issue becomes far more interesting when we look at living things, which are making choices in arenas much closer to what we hold dear.

当安东尼·范·列文虎克将显微镜改进到足以观察单细胞生物时，他注意到细胞以明显有目的的方式迁移。在接下来的几百年里，这些观察结果得到了完善，因为各种研究人员意识到某些类型的细胞和生物会根据环境中的化学信号来控制它们的运动。

When Antonie van Leeuwenhoek perfected the microscope sufficiently to observe single-celled organisms, he noted that cells migrated in apparently purposeful ways. These observations were refined over the next few hundred years as various researchers realized that certain types of cells and organisms were directing their movements according to chemical signals in the environment.

这种现象的通称是趋化性。要了解其工作原理，我们不妨考虑一种低等细菌：大肠杆菌。它的外表面有几根鞭状、半刚性、螺旋状的鞭毛。每根鞭毛都连接到一个可以向任一方向旋转的化学马达上。当鞭毛逆时针旋转时，它们会排成一束螺旋状的鞭毛，从而推动细菌沿直线运动。然而，顺时针旋转会导致鞭毛束断裂，鞭毛会向各个方向摆动，导致细菌随机翻滚。观察细菌时，它的运动在随机翻滚和直线运动之间交替进行。

The general name for this phenomenon is chemotaxis. To understand how it works, consider a lowly bacterium: E. coli. On its outside surface are several whiplike, semirigid, helical flagella. Each flagellum is attached to a chemical motor that can rotate it in either direction. When the flagella rotate counterclockwise, they all align into a single, corkscrew-like bundle, and in doing so propel the bacterium along a straight path. However, clockwise rotation causes the bundle to break apart, and the flagella flail about in all directions, causing the bacterium to tumble randomly. When one observes a bacterium, its motion alternates between these random tumbles and straight runs.

尽管这些行为看起来可能有限，但它们足以让细菌到达它需要去的地方。假设我们将一滴化学物质放入细菌的世界。液滴缓慢扩散形成化学梯度，在液滴放置的地方浓度较高，而远离该点时浓度则降低。假设我们添加的化学物质是一种营养食品，例如糖。一旦液滴开始扩散，我们就会注意到细菌的一些有趣行为。虽然细菌仍然在直线运行和翻滚之间交替，但执行每个动作所花费的时间取决于其前进的方向。当细菌向液滴移动时，它往往花更多的时间直行而不是翻滚。当它远离液滴时，它往往会翻滚更多。这种行为通常会导致细菌沿化学梯度向上移动（见图 6.1）。类似地，如果细菌想要避免某种化学物质，那么当细菌朝向化学物质来源处移动时，它会倾向于翻滚得更多，而当细菌远离化学物质来源处时，它会倾向于翻滚得更少，这样它就会远离浓度最高的区域。

Although those may seem like limited behaviors, they are enough to get the bacterium where it needs to go. Suppose we place a drop of some chemical into the bacterium’s world. The slow dispersal of the drop forms a chemical gradient with a high concentration where we placed the drop and a decreasing concentration as we move away from that point. Assume that the chemical we added is a nutritious food such as sugar. Once the drop begins to disperse, we will notice some interesting behavior on the part of the bacterium. While the bacterium still alternates between straight runs and tumbles, the time spent doing each action varies depending on the direction in which it is heading. When the bacterium is moving toward the drop, it tends to spend more time going straight than tumbling. When it is heading away from the drop, it tends to tumble more. This type of behavior will, in general, cause the bacterium to move up the chemical gradient (see Figure 6.1). Similarly, if the chemical is something that the bacterium wants to avoid, it will tend to tumble more when it is headed toward the source and less when it is headed away, and by doing so it will move away from the area of highest concentration.

图 6.1：模拟细菌利用趋化性寻找目标。细菌从图表左上角的坐标 (0,200) 开始，目标位于右下角 (200,0)。细菌交替进行翻滚（实心圆），将其重定向到随机方向，然后直线运行。直线运行所花费的时间与它遇到的从目标扩散的分子数量的变化成正比——在本模拟中，它由从旧点和新点到目标的距离的逻辑概率函数控制。如图所示，这种简单的行为足以引导细菌朝着目标前进，并使其停留在目标附近。

Figure 6.1: A simulated bacterium using chemotaxis to seek out a goal. The bacterium begins in the upper left part of the diagram at coordinates (0,200), and the goal is located in the lower right (200,0). The bacterium alternates between tumbles (solid circles), which redirect it in a random direction, and straight runs. The time spent in a straight run is proportionate to the change in the number of molecules it encounters diffusing from the goal—in the case of this simulation, it is controlled by a logistic probability function of the distance to the goal from the old and new points. As seen in the figure, this simple behavior is sufficient to direct the bacterium toward, and have it remain around, the goal.

我们知道，细菌没有任何神经元或其他可以构成大脑的明显部分，但它却能够以某种方式向好的东西移动，远离坏的东西。在这种情况下，分子代替了大脑。虽然确切的分子机制和化学反应有点复杂（至少对经济学家来说），但最终细菌是由一个复杂的分子系统通过化学规则相互作用来控制的。

We know that the bacterium doesn’t have any neurons or other obvious parts that could constitute a brain, yet somehow it is able to move toward good things and away from bad ones. In this case, molecules substitute for brains. While the exact molecular mechanisms and chemical reactions are a bit complicated (at least to an economist), in the end the bacterium is controlled by a complex system of molecules interacting with one another through the rules of chemistry.

当两个分子相遇时，其中一个或两个分子都可能发生改变。这些改变与分子的物理形状有关，目前有大量科学研究致力于了解蛋白质链如何折叠成各种分子结构。有时，一个分子可能“适合”另一个分子，导致受体分子发生变化。有时，分子可以相互添加或移除化学基团，大致相当于打开或关闭化学开关。利用这些核心能力，结合数十亿年的进化来调整各种反馈回路和衰减过程，一些相当复杂的行为就会出现。

When two molecules encounter each other, one or both of them may be altered. These alterations are tied to the physical shapes of the molecules, and there is a large amount of science devoted to understanding how chains of proteins fold into various molecular structures. At times, one molecule may “fit” into another, causing the receptor molecule to undergo a change. At other times, molecules can add or remove chemical groups to one another, roughly equivalent to turning on or off a chemical switch. Take these core abilities and mix in a few billion years’ worth of evolution to tune various feedback loops and decay processes, and some rather sophisticated behaviors can emerge.

就简单的趋化性而言，这个过程大致如下。当我们将一滴化学物质放入环境中时，它所含的大量分子（为了便于论述，我们假设为 6 × 10 23左右）会立即开始扩散。随着时间的推移，这种扩散将形成一个梯度，随着我们远离最初的一滴，化学物质的分子数量会越来越少。

In the case of simple chemotaxis, the process is roughly as follows. When we place a drop of chemical into the environment, the enormous number (for argument’s sake, let’s say 6 × 1023 or so) of molecules it contains immediately begin to diffuse. Over time, this diffusion will form a gradient, with fewer and fewer molecules of the chemical as we move away from the initial drop.

当细菌在周围环境中移动时，它会遇到这些分子。细菌的细胞膜外部有受体，这些受体很容易与分子结合——这里的一个常见比喻是将分子视为可以附着并打开锁状受体的钥匙。当分子与受体结合时，它会在细胞内引起一系列化学变化，从而导致细菌的两种重要行为。

As the bacterium moves around in its world, it encounters these molecules. The bacterium has receptors on the outside of its membrane that bind easily with the molecules—a common analogy here is to think of the molecules as keys that can attach to and open the lock-like receptors. When a molecule binds to the receptor, it causes a cascade of chemical changes inside the cell that lead to two important behaviors on the part of the bacterium.

例如，驱虫剂分子结合后引起的第一种行为是，受体在细胞内释放一组新分子——为了避免混淆，我们称这些新分子为信号。这些信号导致细菌发生各种级联反应，传播初始信号，最终导致产生新的短暂信号，使鞭毛马达反转。通常，这些马达逆时针运转（约 6,000 rpm），这意味着沿直线游动，但当马达反转时，鞭毛会完全歪斜，细菌会翻滚。短暂的信号导致翻滚，之后马达很快恢复正常旋转，细菌又回到正轨。如果不是驱虫剂与外部受体结合，而是引诱剂结合，那么产生的反转信号就会减少，细菌翻滚的次数也会减少。因此，分子通路会诱导一种非常适应性的行为：当细菌周围有引诱剂时，它倾向于直线行进，但当遇到驱虫剂时，它会改变方向。

The first behavior caused by the binding of, say, a repellent molecule is that the receptor releases a new set of molecules—to avoid confusion, we will just call these latter molecules signals—inside the cell. These signals lead to various cascades of reactions in the bacterium that propagate the initial signal and eventually cause the production of a new, short-lived signal to be sent that reverses the flagellar motor. Normally these motors run counterclockwise (at around 6,000 rpm), implying swimming in a straight line, but when the motor reverses, the flagella become all askew and the bacterium tumbles. The short-lived signal causes tumbling, after which the motor quickly resumes its normal rotation and the bacterium is back on the straight and narrow. If, instead of a repellent binding to the outside receptor, an attractant binds, then fewer such reversal signals are produced and the bacterium tumbles less. Thus, the molecular pathways induce a very adaptive behavior: when the bacterium is around attractants, it tends to go straight, but when it encounters repellents, it changes directions.

外部分子结合引起的第二种行为涉及外部受体本身的反馈回路。受体的敏感性与外部分子的结合以及由此类结合引起的一些内部变化有关。随着结合的增多，受体对外部分子的敏感性降低，本质上是在短期内（大约一分钟）适应外部化学物质的水平。因此，当引诱剂分子与受体结合时，它既会立即减少翻滚次数（如前所述），又会使受体在随后的短时间内对引诱剂的敏感性降低。如果细菌在接下来的几分钟内遇到类似水平的引诱剂，它将以正常速度翻滚，而不是降低的速度。这种反馈机制使细菌能够“记住”其短期过去。因此，如果它发现自己处于与不久前大致相同的情况，它就会恢复正常行为（偶尔跌倒），并且只有当它检测到相对于最近发生的变化时，它才会改变这种模式。当细菌发现自己处于与过去相同的情况时，这种记忆会诱发其探索行为。

The second behavior caused by the binding of the outside molecule involves a feedback loop on the outside receptor itself. The sensitivity of the receptor is tied to the binding of external molecules and to some internal changes caused by such bindings. As more binding occurs, the receptor desensitizes itself to the outside molecules, essentially adapting—on a short-term basis, over the time span of a minute or so—to the outside level of the chemical. Thus, when an attractant molecule binds to the receptor, it both immediately reduces the number of tumbles (as previously discussed) and makes the receptor less sensitive to the attractant for a short while thereafter. If the bacterium meets a similar level of attractant over the next few minutes, it will tumble at its normal rate rather than the reduced one. This feedback mechanism allows the bacterium to “remember” its short-term past. Thus, if it finds itself in roughly the same situation it found itself in just a short while ago, it reverts to its normal behavior (occasional tumbles), and it alters this pattern only if it detects a change relative to the recent past. This memory induces exploratory behavior in the bacterium when it finds itself in the same situation as in the past.

上文重点讨论了细菌遇到引诱剂或驱虫剂的情况，但如果细菌同时遇到这两种物质，会发生什么情况？在这种情况下，细菌需要权衡引诱剂的潜在益处和驱虫剂的成本，决定采取何种行动。这个问题最早由 Wilhelm 提出1888 年，普费弗 (Pfeffer) 发现了两种梯度的相对强度，这才是关键——如果引诱剂梯度强于驱避剂梯度，细菌就会向前移动，反之，细菌就会远离。因此，当两种梯度同时存在时，细菌能够寻找好东西并避开坏东西，而同样的分子决策过程也能够做出权衡，从而赋予细菌一套偏好。

Above, we focused on the case when the bacterium confronts either an attractant or a repellent, but what happens if it encounters both simultaneously? In such a case, the bacterium needs to decide what to do by making a trade-off between the potential benefits of the attractant and the costs of the repellent. This question was first explored by Wilhelm Pfeffer in 1888, and he found that the relative strength of the two gradients is what matters—if the attractant gradient is stronger than that of the repellent, the bacterium moves forward, and if not, it moves away. Thus, the same molecular decision-making process that allows the bacterium to seek out good things and avoid bad ones is also capable of making trade-offs when both are present, giving the bacterium a set of preferences.

要想在行为复杂性上比我们简单的细菌更进一步，可以考虑变形虫多头绒泡菌，它更广为人知的是一种黏菌。在其生命周期的某个阶段，这种黏菌由一个单细胞实体（至少有多个细胞核）组成，以类似变形虫的方式寻找食物。和我们的细菌一样，这种动物没有神经元，因此其行为也必须由各种分子途径决定。

To move up a notch of behavioral complexity from our simple bacterium, consider the amoeba Physarum polycephalum, better known as a type of slime mold. During one part of its life cycle, this slime mold consists of a single-celled entity (with multiple nuclei, no less) that searches for food in an amoeba-like manner. Like our bacterium, this animal has no neurons, so its behavior must be dictated by various molecular pathways as well.

这种黏菌喜欢食物，但不喜欢光（光除了其他有害影响外，还会破坏其细胞过程）。为了了解其决策过程，澳大利亚的两位研究人员 Tanya Latty 和 Madeleine Beekman（《变形虫的非理性决策》，《皇家学会学报 B》，2011 年）创造了一个环境，其中包含食物和光线量各不相同的斑块。然后，通过将黏菌放入该环境中，他们可以看到它喜欢哪个斑块。

This slime mold enjoys food but dislikes light (which, among other harmful effects, disrupts its cellular processes). As a first step in understanding its decision making, two researchers in Australia, Tanya Latty and Madeleine Beekman (“Irrational Decision-Making in an Ameboid Organism,” Proceedings of the Royal Society B, 2011), created an environment that contained patches that varied in the available amounts of food and light. Then, by introducing a slime mold into this environment, they could see which patch it preferred.

通过混合斑块的条件，他们可以得出黏菌的偏好——例如，为什么黏菌会喜欢高食物和光照，而不是低食物和黑暗？结果表明，饥饿的黏菌喜欢黑暗和高食物的地块，而不是光明和高食物的地块，后者比黑暗和中等食物的地块要好，等等。吃饱的黏菌的偏好略有不同，它喜欢黑暗和高食物的地块，而不是黑暗和中等食物的地块，后者比光明和高食物的地块要好，等等。这些测试和其他测试表明，黏菌的分子决策机制似乎能够在不同程度的好事和坏事之间做出合理的权衡。此外，它还表明了黏菌的内部状态如何影响这些偏好：当它挨饿时，它会用额外的风险（以暴露在更多光照下的形式）来换取额外的食物。

By mixing the conditions of the patches, they could derive the preferences of the slime mold—for example, does it prefer high food and light over low food and darkness? It turns out that a starved slime mold prefers a dark and high-food patch to a light and high-food patch, which is better than a dark and medium-food patch, and so on. A well-fed slime mold has slightly different preferences, preferring a dark and high-food patch to a dark and medium-food patch, which is better than a light and high-food patch, and so on. These and other tests reveal that the slime mold’s molecular decision-making mechanism seems to be able to make reasonable trade-offs between various levels of good and bad things. Moreover, it demonstrates how those preferences can be influenced by the slime mold’s internal state: when it is starved, it will trade off additional risk (in the form of being exposed to more light) for extra food.

这似乎很合理，但让我们考虑一下在更复杂的环境中的决策。众所周知，人类经常违反看似合理的决策原则。例如，假设你让某人在一家食物美味但位置糟糕的餐厅（Dive）和一家食物糟糕但位置优越的餐厅（Tourist Trap）之间做出选择。通过调整这两家餐厅的食物和位置质量，我们可以创造一种情况，即一个人对于去 Dive 还是 Tourist Trap 都无所谓。现在，增加第三家明显不如 Dive 的餐厅——例如，位置相同但食物稍差一些。先验地，你可能会预测，这样的增加不会对 Dive 产生任何影响。个人的最终选择，因为新选项比已有选项更差，因此应立即将其视为无关选项而丢弃。然而，研究表明，增加这种无关选项实际上会改变人们的行为，导致他们现在更喜欢 Dive 而不是旅游陷阱（见图 6.2）。营销人员非常清楚这种吸引力效应，通常会推出劣质产品来提高现有产品的销量。顺便说一句，还有其他操纵手段，比如推出另一家与 Dive 类似的餐厅，但在某个方面略胜一筹（比如，食物略好），而在另一个方面略差（位置略差），这也会以意想不到的方式改变决策（在这种情况下，消费者现在更喜欢旅游陷阱）。

This seems rational enough, but consider decision making in more complicated settings. It is well known that humans often violate what seem to be reasonable tenets of decision making. For example, suppose you give someone a choice between dining at a restaurant with good food and a crummy location (the Dive) or one with crummy food and a great location (the Tourist Trap). By tinkering with the food and location qualities between these two places, we can create a situation in which an individual is indifferent about whether she goes to either the Dive or the Tourist Trap. Now, add a third restaurant that is clearly inferior to the Dive—for example, the same type of location but slightly worse food. A priori, you might predict that such an addition will make no difference to the individual’s final choice, since the new option is inferior to an already existing choice, and thus it should be immediately discarded as irrelevant. However, studies show that the addition of such an irrelevant alternative actually alters people’s behavior, causing them now to favor the Dive over the Tourist Trap (see Figure 6.2). Marketers are well aware of this attraction effect and will often introduce an inferior product to boost sales of an existing one. By the way, there are other manipulations one can do, such as introducing another restaurant that is like the Dive but is a bit better on one dimension (say, slightly better food) and a bit worse on the other (slightly worse location), that will also alter decision making in unexpected ways (in this case, making consumers now prefer the Tourist Trap).

事实证明，黏菌和人类一样，也会犯同样的决策错误。首先创建两个斑块，一个是黑暗的，食物很少，另一个是明亮的，食物较多，这样黏菌对每个斑块的选择就大致相同。现在引入第三个较差的选择（例如，一个黑暗的斑块，食物比先前存在的黑暗斑块还要少）。尽管这个新斑块比现有斑块之一更差，因此应该与两个先前存在的选择无关，但我们发现，它会导致黏菌倾向于选择先前存在的黑暗斑块，而不是光线和食物较多的斑块（至少在它们没有挨饿的情况下）。

It turns out that slime molds fall prey to the same decision errors that humans do. Start by creating two patches, one that is dark with little food and one that is light with more food, such that the slime molds choose each one about equally. Now introduce a third, inferior option (such as a dark patch with even less food than the preexisting dark patch). Even though this new patch is inferior to one of the existing patches and thus should be irrelevant to the two preexisting choices, we find that it causes the slime molds to gravitate to the preexisting dark patch over the one with more light and food (at least if they are not starved).

图 6.2：两家餐厅，Dive 和 Tourist Trap，在两个维度上存在差异，以至于人们对这两家餐厅无感（左图）。增加一个不相关的替代方案（在本例中，一家在两个维度上都比 Dive 差的餐厅）会导致偏好转向 Dive 而不是 Tourist Trap（右图）。

Figure 6.2: Two restaurants, the Dive and the Tourist Trap, differ across two dimensions in such a way that people are indifferent between the two (left panel). The addition of an irrelevant alternative (in this case, a restaurant that is inferior to the Dive on both dimensions) causes a shift in preferences to favor the Dive over the Tourist Trap (right panel).

我们对黏菌选择背后的机制知之甚少。很可能是某种分子机制在起作用，这种机制可能与我们在趋化性中看到的类似。无论如何，黏菌和细菌都可以做出有效的决定，尽管它们之间没有神经元。

Not much is known about the mechanisms that underlie the slime mold’s choices. It is likely that some molecular mechanism, perhaps similar in spirit to what we see in chemotaxis, is at play here. Regardless, both slime molds and bacteria, without a neuron to be had between them, can make productive decisions.

根据所处环境改变行为并（至少大多数时候）做出适当权衡的能力对于生存至关重要。尽管这种行为复杂性看起来很复杂，但不难想象这种机制是如何进化的。从细胞外获取分子（如营养物质）并将其运输到细胞内的细胞机制是生命的基本组成部分。如果选择性运输是有益的，那么具有更具体的运输机制（例如，只移动特定类型的分子）的细胞更有可能存活下来。从如此简单的开始，很容易开发出受体，这些受体不是将特定分子运输到细胞内，而是通过发出细胞内信号来传达外部分子的存在。从这里开始，让这些信号诱导有效的内部动作（例如控制鞭毛的旋转）、以有用的方式级联或降解，甚至向初始受体提供反馈，这并不是一个很大的飞跃。

The ability to change behavior depending on the environment one encounters and to make (at least most of the time) appropriate trade-offs is crucial for survival. As complicated as this behavioral complexity seems, it’s not hard to imagine how such mechanisms could evolve. Cellular mechanisms that take molecules from outside the cell, such as nutrients, and transport them into the cell are a fundamental part of life. Cells with more specific transport mechanisms that, say, move only particular types of molecules are far more likely to survive if the selective transport is beneficial. From such simple beginnings, it is easy to develop receptors that, instead of transporting specific molecules into the cell, just communicate the outside molecule’s presence by emitting an intracellular signal. From here, it is not a great leap to have such signals induce productive internal actions (such as controlling the rotation of the flagella), cascade or degrade in useful ways, and even provide feedback to the initial receptor.

综上所述，我们在这些单细胞中观察到的行为相当复杂。然而，人们很容易轻视细菌的成就，声称这只是一组简单的分子反应的结果，因此微不足道，不应被视为任何真正的思维形式。当然，由神经元组成的大脑必须提供更深层次的思维形式。

All things considered, the behavior we observe in these single cells is fairly sophisticated. Nevertheless, it is tempting to minimize the bacterium’s accomplishment by claiming that because it is only the result of a set of straightforward molecular reactions, it is therefore trivial and should not qualify as any real form of thinking. Surely brains composed of neurons must provide a deeper form of thinking.

但是，除了人类比大多数其他物种拥有更多的神经元之外，神经元还有什么特别之处呢？神经元真正擅长的是远距离传输信号。我们的细菌相对较小，因此漂浮并随机碰撞的分子足以传输信号，因为即使是随机漂移的物体也会在如此小的尺度上经常碰撞。然而，随着生物体变大，它需要一种更可靠、更快速的机制来远距离传递信号——“当它绝对、肯定必须存在时”，你需要像神经元这样的东西来快速传输和连接信号。除了规模的必要性之外，这些系统之间可能没有太大区别。事实上，分子决策机制导致对理性决策和与人类完全发育的神经系统所犯的错误相似的错误进行研究发现，这两个系统可能由相似的原理驱动。

But what is so special about neurons anyway, other than that humans tend to have more of them than most other species? What neurons are really good at is transmitting signals across large distances. Our bacterium is relatively tiny, so molecules floating around and randomly bumping into one another are sufficient to transmit signals, as even randomly drifting things bump into one another quite often on such small scales. However, as an organism gets bigger, it needs a more reliable and rapid mechanism to convey signals across large distances—“when it absolutely, positively has to be there,” you need something like a neuron to quickly transmit and connect signals. Other than the necessities of scale, there may not be much difference between these systems. Indeed, the fact that molecular decision mechanisms lead both to rational decisions and to errors similar to the ones humans make with fully developed nervous systems suggests that the two systems may be driven by similar principles.

如果这是真的，那么思维可能存在于比我们通常想象的更广泛的范围内。如果简单的分子机制允许细菌、黏菌和它们的同类拥有相当复杂的行为，我们可能想要研究其他信号和反应系统，看看它们是否也包含思维。也许任何一组相互作用的分子都可以被解释为执行类似思维的计算。

If that is true, it may be the case that thinking exists on a much broader scale than we normally imagine. If simple molecular mechanisms allow bacteria, slime molds, and their lot to incorporate fairly sophisticated behavior, we might want to examine other systems of signals and reactions to see if they, too, embrace thinking. Perhaps any set of interacting molecules can be interpreted as performing a thinking-like computation.

此外，如果信号和反应就是思考所需要的全部，那么大脑可能并不局限于个人。也许更大规模的社会系统，如蜂巢中的蜜蜂、组织中的人们或相互关联的市场集合，可能正在进行类似思考的计算。我们将在下一章探讨这个主题。

Moreover, if signals and reactions are all that are needed for thinking, then brains may not be restricted to individuals. Perhaps larger-scale social systems, such as honeybees in a hive, people in an organization, or a collection of interconnected markets, may be performing thinking-like computations. We’ll explore this topic in the next chapter.

我们的周围很可能到处都是大脑，其中一些我们很容易识别和钦佩，而另一些我们才刚刚开始了解。

We likely are surrounded by brains everywhere, some of which we easily recognize and admire and others of which we are only beginning to understand.

七

seven

从蜜蜂到大脑：群体智慧

From Bees to Brains: Group Intelligence

蜜蜂就是这样工作的，它们按照自然界的规律，向人类王国传授秩序行为。

For so work the honey-bees, creatures that by a rule in nature teach the act of order to a peopled kingdom.

—威廉·莎士比亚

—William Shakespeare

碳想象一下，我们偶然遇到了一个外星生物。它有一个外膜，可以包裹住内部，同时又能与外界隔绝。当潜在的捕食者接近时，它能够发出有毒的抛射物来驱赶它们。在生物体内，数以万计的粒子发挥着各种功能，包括将这种显然是温血生物的内部温度保持在一个狭窄的范围内，将废物输送到外界，产生新粒子并维持旧粒子，以及许多其他生存所必需的内部过程。生物体可以向外界伸出细长的卷须，随意摸索，似乎是为了寻找营养物质。一旦卷须偶然发现了丰富的营养来源，生物体就会伸出额外的卷须，直接前往该位置，帮助将发现的东西运回。进入的营养物质通过各种过程转化为可储存的能量，可用于维持生物体的生命（就像我们自己的细胞将葡萄糖等分子转化为 ATP 一样）。最后，我们发现生物体中有一种特定的粒子似乎起着类似于我们自己的 DNA 的作用，因为它包含了创建对生物体活力至关重要的其他粒子的恒定流所需的信息。

Consider for a moment happening upon an alien organism. It has an outer membrane that contains its insides while also keeping the outside world at bay. When potential predators approach, it has the ability to send out poisonous projectiles to repel them. Inside the organism, tens of thousands of particles perform a variety of functions, including maintaining this apparently warm-blooded organism’s interior temperature within narrow bounds, transporting waste products to the outside world, creating new particles and maintaining old ones, and many other internal processes necessary for survival. The organism can send out into the world long, thin tendrils that grope randomly about, apparently in search of nutrients. Once a tendril happens upon a rich source of nutrients, the organism sends out additional tendrils that go directly to this location to help transport back the find. Incoming nutrients are converted by various processes into a form of storable energy that can be used to keep the organism alive (much the way our own cells convert molecules such as glucose into ATP). Finally, we find that there is one specific particle in the organism that appears to serve a role akin to our own DNA, as it contains the needed information to create a constant stream of the other particles critical to the organism’s vitality.

随着我们在一年中继续观察这种生物，我们注意到一个有趣的现象。通常在春季，这种生物似乎会喷出大约一半的颗粒，然后这些颗粒会沉淀在附近的一个地方。卷须也从这团物质中冒出来，但它们似乎不是在寻找营养物质，而是在寻找新的外膜——就像寄居蟹寻找新壳一样。我们观察到，连接物质和潜在膜的卷须要么变强，要么枯萎，直到最终只剩下一根结实的卷须。此时，这根卷须似乎将整个物质拉进了它的新皮肤。通过这个过程，最初是一个单一的生物体分裂成两个。这两个新形成的生物体回到了生存的必需品，寻找新的营养来源，不断增强，并且，如果条件保持有利，就会重新分裂。

As we continue to observe the organism over the course of a year we notice an interesting phenomenon. Typically during the spring, the organism appears to erupt about half of its particles, which then settle in a nearby location. Tendrils emerge from this mass, too, but rather than seeking out nutrients they seem to be searching for a new outer membrane—much the way a hermit crab seeks a new shell. As we watch, the tendrils connecting the mass to potential membranes either strengthen or wither away, until eventually only one strong tendril remains. At this point, it is as if this tendril pulls the entire mass of particles into its new skin. Through this process, what started out as a single organism has divided into two. These two newly constituted organisms return to the necessities of survival, seeking out new sources of nutrients, growing in strength, and, if conditions remain favorable, dividing anew.

上述生物并非某种奇怪的新形式的外星生命，而是一群蜜蜂，从远处看很难分辨出单个蜜蜂。这一新观点表明，将一群蜜蜂视为一个单一的超级有机体，而不是成千上万只蜜蜂，可能会有所帮助。

The organism described above is not some strange new form of extraterrestrial life but rather a colony of honeybees viewed from enough distance that we have difficulty making out the individual bees. This new point of view suggests that it may be useful to think of a hive of honeybees as a single superorganism, rather than as tens of thousands of individual bees.

这样的超级有机体是如何运作的？当我们通常想到蜂巢时，很容易将其视为一个君主制国家，由一位仁慈的女王统治，女王指挥着她的工人们完成日常工作，包括采集花蜜和花粉、加工和储存蜂蜜，以及维持蜂巢生存的所有其他职责。唉，这个关于一个精心调配的贵族政权的令人欣慰的故事与事实相去甚远，尽管这里的现实要丰富、迷人和实用得多。

How does such a superorganism function? When we normally think of a hive, it is all too easy to view it as a monarchy ruled by a benevolent queen, who directs her workers on the daily tasks of gathering nectar and pollen, processing and storing honey, and all of the other duties that keep the hive alive. Alas, this comforting story of a finely tuned aristocracy could not be further from the truth, though the reality here is far more rich, fascinating, and useful.

正如我们在第 6 章中看到的，即使是通过一组固定的化学规则相互作用的分子集合也可以表现出智能行为，例如细菌寻找好东西并避开坏东西。鉴于分子相互作用可以为细胞提供做出智能决策的能力，那么其他类型的粒子（这里是蜜蜂）的相互作用也许也可以赋予这些系统智能。正如我们将看到的，蜜蜂的真实情况将帮助我们揭开其他分散的、相互作用的粒子系统的奥秘，这些粒子正在做出智能决策，从从细胞中的分子到大脑中的神经元、蜂群中的蜜蜂、市场中的商人、公司中的员工等等。

As we saw in Chapter 6, even collections of molecules interacting via a fixed set of chemical rules can display intelligent behavior, like a bacterium seeking out good things and avoiding bad ones. Given that molecular interactions can provide a cell with the ability to make intelligent decisions, then perhaps interactions of other types of particles, here honeybees, could bestow intelligence on those systems as well. As we will see, what’s true of honeybees will help us unlock the mysteries of other systems of decentralized, interacting particles that are making intelligent decisions, from molecules in cells to neurons in brains, bees in colonies, traders in markets, workers in firms, and beyond.

蜜蜂群在春夏两季生机勃勃，但在冬季，随着气温下降，花蜜停止流动，它们往往处于生存边缘。为了成功过冬，蜂巢必须有足够的工蜂来维持温度，并在春季花蜜开始流动时迅速重新繁殖，但过多的工蜂会在冬季结束前耗尽有限的蜂蜜储备。因此，蜂群必须小心控制其规模。

Honeybee colonies, while vibrant during the spring and summer, are often on the edge of survival during the winter as temperatures drop and nectar ceases to flow. To successfully overwinter, the hive must have enough workers to maintain its temperature and to rapidly repopulate the colony when the nectar begins to flow in the spring, but too many workers will exhaust the limited stores of honey before winter ends. Thus, colonies must carefully control their size.

图 7.1：一群野生蜜蜂聚集在我卡内基梅隆办公室走廊对面的一栋建筑的屋檐下。经过多日的无果寻找新家后，蜜蜂开始在这个暴露的地方筑巢。几周后，蜜蜂消失了。（作者拍摄。）

Figure 7.1: A swarm of wild honeybees that formed under the eave of a building just down the hall from my Carnegie Mellon office. After many days of an unsuccessful search for a new home, the swarm began to build the comb in this exposed location. After a few weeks the swarm disappeared. (Photograph by the author.)

分蜂通常发生在春季，此时花蜜充足，蜂蜜储存充足，蜂群迅速壮大。当蜂群分蜂时，老蜂王会带着大约一半的蜂群离开。离开的工蜂会分得一部分蜂蜜，然后蜂群就会在附近停留（见图 7.1）。蜂王会挤在蜂群中间，此时蜂群处于脆弱状态，因为蜂群会面临天气变化和掠食者的威胁。当蜂群安顿下来后，几只侦察蜂会出发寻找潜在的筑巢地点——可能是树洞或建筑物的空洞。当侦察蜂找到可能的地点时，它会对其进行探索并评估其整体质量。 （通过一系列巧妙而繁琐的实验，我们现在对侦察蜂在新家中所寻求的品质有了很好的了解。具体来说，它们想要一个大小合适的洞穴、一定的离地高度以及一定大小和方向的入口。）一旦侦察蜂探索到某个地点，她就会返回蜂群，并开始通过在蜂群外表面上表演的摇摆舞向其他侦察蜂传达该位置。这一步的关键是跳舞的时间与侦察蜂对地点质量的感知有关，质量越高的地点跳舞的时间就越长。蜂群中的其他侦察蜂观察舞蹈，并被诱导亲自检查广告中的位置。

Swarming typically occurs in the spring, when nectar is plentiful, honey has been stored, and the colony is rapidly growing. When the colony swarms, the old queen takes off with roughly half of the hive. The exiting workers take their share of honey, and the resulting swarm alights nearby (see Figure 7.1). The swarm, with the queen huddled in the middle, is vulnerable at this time, as it is exposed to the vagaries of weather and predation. As the swarm settles in, a few scouts head off and search for potential nesting sites—perhaps a hollow in a tree or a cavity in a building. When a scout finds a possible site, she explores it and makes an evaluation of its overall quality. (Through a clever set of tedious experiments, we now have a good sense of the qualities that scouts are seeking in a new home. In particular, they want some combination of a properly sized cavity, a certain height above the ground, and an entrance of a certain size and orientation.) Once a scout explores a particular site, she returns to the swarm and begins to communicate the location to the other scouts by way of a waggle dance performed on the outside surface of the swarm. The key to this step of the process is that the time spent dancing is tied to the scout’s perception of the quality of the site, with higher-quality sites receiving longer dances. Other scouts on the swarm observe the dancing and are induced to check out the advertised location for themselves.

正是在这个关键时刻，我们第一次意识到这样一个去中心化系统是如何运作的。由于被认为更好的地点会接受更长的舞会，而且新的侦察员是通过观察舞会招募的，因此更有可能将新兵派往潜在的更好地点。这会导致对更高质量地点的正反馈循环。即使有这种正反馈，这个系统中也有一个微妙的机制可以防止过快地陷入错误的选择。由于潜在的更好地点被探索得更频繁，它们会收到更多的质量评估，所以即使最初的侦察员对地点的真实质量的判断不太准确，后续的调查也会倾向于纠正这种错误。

It is at this juncture that we get our first hint about how such a decentralized system could possibly work. Since the sites that are perceived to be better receive longer dances, and since new scouts are recruited by observing the dances, it is more likely that recruits will be sent to the potentially better locations. This results in a positive feedback loop for the higher-quality sites. Even with this positive feedback, there is a subtle mechanism built into this system that prevents locking into a bad choice too quickly. Since potentially better sites are explored more often, they receive many more evaluations of quality, so even if the initial scouts are somehow poorly calibrated about the site’s true quality, subsequent investigations will tend to correct such errors.

想象一下观察舞者群的外部并跟踪舞者所宣传的地点。当舞者群第一次降落时，我们看不到任何活动，除了侦察员朝随机方向前进。当第一个侦察员返回时，她会为发现的任何地点跳舞，也许这会促使其他侦察员亲自去看看。很快，其他侦察员从最初的探索中返回，并宣传新的地点。随着时间的推移，我们开始看到几个网站被宣传，我们甚至可以通过计算给定时间间隔内的舞者数量来跟踪网站的受欢迎程度。就像Billboard音乐排行榜一样，我们看到一些网站已经上榜了几个时期，新网站偶尔会突然闯入排行榜，而有时，曾经流行的网站就像昙花一现一样从神坛上​​跌落，再也没有人听说过。

Imagine observing the outside of the swarm and tracking what locations are being advertised by the dancers. When the swarm first alights, we see no activity other than scouts heading off in random directions. As the first scout returns, she dances for whatever location was uncovered, and perhaps this induces some other scouts to go see it for themselves. Soon other scouts return from their initial forays, and new locations are advertised. Over time we start to see several sites being advertised, and we could even track a site’s popularity by counting the number of dancers over some given time interval. Like the Billboard music charts, we see some sites that have been charting for a few periods, with new sites occasionally breaking into the mix rising with a bullet and, at times, once popular sites falling from grace like one-hit wonders, never to be heard from again.

这种机制允许蜂群进行多次并行搜索，并相对快速地找到新家。没有中央会计记录每个侦察员的发现并决定将下一个侦察员派往何处或何时结束搜索并移动。相反，侦察员根据自己对蜂群表面小社区发生的事情的本地观察来指挥。该系统有各种间接制衡措施，例如更深入地调查更有希望的地点，同时保留各种其他选择。

This mechanism allows the swarm to conduct many parallel searches and to find a new home relatively quickly. There is no central accountant noting each scout’s findings and deciding where to send the next scout or when to end the search and move. Rather, scouts are directed by their own, local observations of what is happening in their small neighborhood on the swarm’s surface. The system has various indirect checks and balances, such as more intensively investigating the more promising sites while also maintaining a variety of other options.

经过一两天的舞蹈表演，一个地点开始成为最受欢迎的地点（见图 7.2）。此时，分散式系统基本上已经做出了选择。

After a day or two of dances, one location begins to emerge as the favorite (see Figure 7.2). At this point, the decentralized system has essentially made its choice.

这个最终选择是如何最终确定并传达给蜂群的？虽然所有蜜蜂都可能以某种方式感觉到舞蹈已经汇聚，但这会削弱任何由本地通信控制的分散系统的合理概念。正是在这里，我们的故事中出现了第二个关键要素，它具有 Shaker 椅子的简单性和纯粹的功能性。最终决定不是由蜂群表面的任何动作驱动，而是在发现的地点做出。研究表明，探索地点的侦察蜂能够感知到大约 20 只蜜蜂的法定人数何时形成，而这种法定人数的出现会触发最终决定。一旦在新地点出现法定人数（请注意，考虑到聚集的侦察蜂本地可获得的信息，感知到这种法定人数并不那么困难），所有侦察蜂都会返回蜂群，开始发出特定的声音（称为吹奏），并进行“嗡嗡声”，类似于一些疯狂的励志演说家穿过观众席。这促使蜂群中的蜜蜂热身飞行肌肉，并准备采取重大行动。

How is this ultimate choice finalized and communicated to the swarm? While it might be possible for all of the bees to somehow sense that the dances have converged, this strains any reasonable notion of a decentralized system governed by only local communication. It is here that the second key element emerges in our story, one that has the simplicity and pure functionality of a Shaker chair. Rather than being driven by any action on the surface of the swarm, the final decision is made at the discovered site. Studies have shown that scouts exploring a site have the ability to sense when a quorum of around twenty bees has formed, and it is the occurrence of such a quorum that triggers the final decision. Once a quorum is present at the new site (note that sensing such a quorum is not all that difficult given the information locally available to the congregating scouts), all of the scouts return to the swarm and begin to make specific noises (known as piping) and perform “buzz runs” that are akin to some crazed motivational speaker running through an audience. This causes the honeybees in the swarm to warm up their flight muscles and get ready to make the big move.

图 7.2：一组时间序列的面板，表示在实际蜂群表面的不同蜂巢位置跳舞的蜜蜂数量。每个箭头代表到潜在蜂巢位置的方向和距离，箭头的宽度表示该特定位置的跳舞次数。蜂群在搜索过程中确定了 11 个不同的位置。最终，蜂群开始集中在位置 B 和 G，在第二天因下雨而暂停后，位置 G 成为一致选择。（数据和图表由 Thomas Seeley 提供。）

Figure 7.2: A time series of panels representing the number of honeybees dancing for various hive locations on the surface of an actual swarm. Each arrow represents the direction and distance to a potential hive site, with the width of the arrow indicating the number of dances for that particular site. The swarm identifies eleven different sites during the search. Eventually the swarm begins to concentrate on sites B and G, and after a pause due to rain on the second day, site G becomes the consensus choice. (The data and figure are courtesy of Thomas Seeley.)

剩下的问题就是，几十只知道去哪里的蜜蜂如何引导数千只不知道去哪里的蜜蜂。这一难题的答案是，少数几只方向正确、行动迅速的蜜蜂就足以引导大量行动缓慢的蜜蜂找到新家。

All that remains is the issue of how a few tens of bees that know where to go can lead a few thousand that do not. The answer to this quandary turns out to be that a handful of well-directed and fast-moving bees is sufficient to direct the large, slower-moving swarm to its new home.

罗素·戈尔曼、戴维·哈格曼和我以一种简单的方式模拟了上述分散决策系统。设想一个瓮中盛有代表每个潜在地点的不同颜色的球。我们将这些球混合在一起，然后盲目地伸手进去挑选一个。我们挑选的颜色就是我们要调查的选项，然后我们将选中的球放回瓮中，并添加更多相同颜色的球。额外球的数量取决于我们挑选的颜色的“质量”。例如，假设瓮中有四种不同的颜色，每当我们挑选一个红色球时，我们都会放回它，并放两个新的红球（类似于侦察兵在参观一个好地点后跳更长的舞），而每当我们挑选任何其他颜色时，我们都会将其替换并只添加一个相同颜色的新球。更换球后，我们再次将球混合并重新抽取。

Russell Golman, David Hagmann, and I have modeled the decentralized decision system above in a simple way. Consider an urn filled with one differently colored ball for each potential site. We mix these balls about and then blindly reach in and pick one. Whatever color we pick is the option we investigate, and we then place the chosen ball back in the urn and also add more balls of the same color. The number of additional balls depends on the “quality” of the color that we picked. For example, suppose we have four different colors in the urn and whenever we pick, say, a red one, we put it back with two new red balls (similar to how a scout does a longer dance after visiting a good site), while whenever we pick any of the other colors, we replace it and add only one new ball of the same color. After we replace the balls, we mix the balls up again and draw anew.

这个瓮的过程与蜜蜂系统中发生的过程类似。在这个过程的任何阶段，挑选特定颜色（潜在地点）的可能性取决于瓮中该颜色的比例。当我们第一次到达放入箱子中，我们有同等的机会挑选任何颜色。一旦我们做出第一个选择，替换后续球的方案就会产生类似于跳舞侦察兵的效果，因为更好的选择（这里是红球）会比其他颜色的球更多地被放回瓮中。这增加了将来选择更好选项的可能性。一旦特定颜色的球数等于或超过预设的法定人数，系统就会做出选择。

This urn process is similar to what happens in the honeybee system. At any stage of the process, the likelihood of picking a particular color (potential site) depends on the proportion of that color in the urn. When we first reach into the bin, we have an equal chance of picking any color. Once we make our first choice, the scheme for replacing subsequent balls has an effect similar to the dancing scouts, as the better option (here, the red ball) gets more balls added back into the urn than the other colors. This increases the likelihood that the better option will be chosen in the future. The system makes a choice as soon as the number of balls of a particular color equals or exceeds a preset quorum level.

图 7.3 显示了该模型的行为。由于我们一开始每种颜色都有一个球，如果法定人数为两个，那么我们首先挑选的颜色球将成为最终选择，因为增加一个（或两个）相同颜色的新球将达到阈值。因此，在法定人数为两个的情况下，选择四种颜色中的任何一种的几率（25%）是相等的。随着法定人数的增加，基于颜色的球的差异增加（最好的球得到两个，其他球得到一个）开始变得更加重要，系统更有可能选择最佳选择。例如，在法定人数为五时，系统选择最佳选择的几率约为 50%。在法定人数为二十时，选择最佳选项的几率为 70%。我们可以通过数学证明，随着我们增加所需的法定人数，系统更有可能选择最佳选项（并且当我们允许阈值无限制地增加时，系统总是会收敛到最佳选项）。

The behavior of this model is shown in Figure 7.3. Since we start with one ball of each color, if the quorum is two, then whatever color ball that we pick first will become the final choice, as the addition of a new ball (or two) of that same color will meet the threshold. Thus, with a quorum of two, there is an equal chance (25 percent) of choosing any of the four colors. As the quorum increases, the differential addition of balls based on color (the best getting two, the others getting one) begins to matter more and the system becomes more likely to pick the best choice. For example, at a quorum of five, the system picks the best choice about 50 percent of the time. At a quorum of twenty, there is a 70 percent chance of picking the best option. We can prove mathematically that as we increase the required quorum, the system is more likely to pick the best option (and as we allow the threshold to increase without bounds, the system always converges to the best option).

图 7.3：在给定不同群体阈值（ x轴）的情况下，瓮中有四种不同颜色时，群体形成最佳选择的可能性（y轴） 。此处，只要选择了最佳颜色，我们就会在瓮中添加两个相同颜色的球，而选择任何其他颜色只会添加一个相同颜色的球。随着所需群体规模的增加，选择最佳选择的可能性也会增加，但达到该群体所需的时间（未显示）也会增加。

Figure 7.3: Likelihood of a quorum forming for the best choice (y-axis) with four different colors in the urn given different quorum thresholds (x-axis). Here, anytime the best color is chosen we add two additional same-­colored balls to the urn, while choosing any of the other colors results in the addition of only one same-colored ball. As the required quorum size increases, the likelihood of picking the best choice increases, but so does the time that it takes (not shown) to reach that quorum.

这种去中心化系统存在一个重要的权衡：随着所需法定人数的增加，时间也会增加达到法定人数所需的时间。因此，如果我们希望系统做出更好的选择，我们需要等待更长时间。通常，等待是昂贵的，特别是在像我们的蜜蜂群这样的系统中，它很容易受到自然因素和捕食者的攻击，而且在目前的配置下，它无法制造和储存蜂蜜。蜂群通常只有几天的时间来寻找新家，否则它们就会受到严重损害，以至于它们的继续生存的可能性不大。因此，等待太久可能比选择一个较差的选择更糟糕。鉴于此，我们可能期望进化会导致令人满意的所需群体水平——也就是说，这会导致蜜蜂选择一个合理的，即使不是最佳的家园，而不是等待太久。看来，蜂群使用的群体阈值约为 20，根据我们的模型，这会导致一种机制，该机制可以相对较快地找到最佳家园，虽然不是完美的。

There is an important trade-off in this decentralized system: as the required quorum level increases, so does the time needed to hit that quorum. Thus, if we want the system to make better choices, we need to wait longer. Typically, waiting is costly, especially in a system such as our honeybee swarm, which is quite vulnerable to the elements and predators and which cannot, in its current configuration, make and store honey. Swarms usually have only a few days to find a new home before they are so compromised that their continued survival is unlikely. Thus, waiting too long may be worse than picking an inferior choice. Given this, we might expect that evolution would result in required quorum levels that satisfice—that is, that cause bees to choose a reasonable, even if not optimal, home rather than wait too long. It appears that swarms use quorum thresholds of around twenty, and given our model, this results in a mechanism that works relatively quickly with a good, but not perfect, chance of finding the best home.

上述分散式决策系统的另一个有趣特征是它如何衡量风险选择。获取决策者风险偏好的典型方法是让他们在安全选择和（就预期值而言）等价的风险选择之间做出选择。例如，假设您下注的平均收益为 2 美元。但是，您可以选择如何获得该平均值：肯定赢 2 美元，或者赌一把 50% 的时间能赢 1 美元，50% 的时间能赢 3 美元。您会选择哪一种？如果第二次赌博有 80% 的机会赢 1 美元，有 20% 的机会赢 6 美元，您的选择会改变吗？

Another interesting feature of the above decentralized decision-making system is how it weighs risky choices. A typical way to derive the risk preferences of decision makers is to give them choices between a safe alternative and an equivalent (in terms of expected value) risky one. For example, suppose you have a bet that on average pays $2. You have a choice of how you can get that average value, however: win $2 for sure or take a gamble that 50 percent of the time pays $1 and 50% of the time pays $3. Which would you pick? If the second gamble had an 80 percent chance of paying $1 and a 20 percent chance of paying $6, would your choice change?

图 7.4：选择安全选项（肯定是 2）与选择风险选项（获得 1 或高于 2 的值的各种概率，使得赌博的期望值始终为 2 — 例如，在最上面的赌博中，获得 1 的概率为 80%，获得 6 的概率为 20%）的概率。只要所需的法定人数大于 2，那么（除了一个例外）系统就更有可能选择安全选项而不是风险选项，因为该结果的概率超过 0.50。随着赌博的风险越来越大（右侧的图例按从风险最大的顶部到底部的顺序排列），系统会通过更频繁地选择安全选项来显示风险规避的增加。

Figure 7.4: Probability of choosing the safe choice (2 for sure) versus the risky choice (various probabilities of receiving either 1 or a higher value than 2, such that the expected value of the gamble is always 2—for example, in the topmost gamble, there is an 80 percent chance of receiving 1 and a 20 percent chance of receiving 6). As long as the required quorum is greater than 2, then (with one exception) the system is more likely to take the safe choice instead of the risky one, since the probability for that outcome is over 0.50. As the gambles become more risky (the legend on the right is ordered from most risky at top to least risky at bottom), the system displays increased risk aversion by choosing the safe option more often.

在图 7.4 中，我们展示了我们的瓮是如何做出这样的选择的。系统必须在肯定收到两个额外的球和右侧图例中所示的一个冒险赌注之间做出选择。虽然所有赌注的预期值都是 2，但赌注的方差（风险的代表）从上往下移动时会减小。该图在 y 轴上显示了选择安全选项的可能性，因此只要该值高于 0.50，系统就是风险规避型的。只要阈值超过 2，瓮系统就更有可能在除一种古怪情况外的所有情况下选择安全选择而不是风险选择，并且随着赌博的方差增加，系统会更加倾向于安全选择。因此，只要我们能够使用瓮捕捉其行为，群体使用的分散式决策系统就是风险规避型的。

In Figure 7.4 we show how our urn makes such choices. The system must pick between receiving two additional balls for sure or one of the risky gambles shown in the legend on the right. While all of the gambles have an expected value of 2, the variance—a proxy for riskiness—of the gambles decreases as you move from the top down. The graph shows the likelihood of picking the safe choice on the y-axis, so anytime this is above 0.50 the system is risk averse. As soon as the threshold exceeds 2, the urn system is more likely to choose the safe choice over the risky one in all but one quirky case, and as the variance of the gamble increases, the system prefers the safe choice even more. Thus, the decentralized decision system used by the swarm, insofar as we can capture its behavior using our urn, is risk averse.

风险规避可能是进化系统中的一个重要策略，因为一个物种繁殖失败，就会将其从进化树上剪掉。你是生命起源以来一长串成功交配的结果。这条链条上只要有一个环节断裂，你就不会在这里了。当然，你不在了和智人灭绝是有区别的，但总体思路仍然适用。一种依赖于赌博而不是稳妥行事的进化策略，实际上风险很大。在某些情况下，赌运气可能有意义，但失败的巨大代价——灭绝就像钻石一样，是永恒的——可能会将这种策略限制在非常特殊的条件下。通常，稳扎稳打才能赢得进化竞赛。以蜜蜂蜂巢为例，分裂蜂巢需要巨大的投资。鉴于此，进化的成功来自于找到一个合理的家园，而不是冒险，让蜜蜂有较小的机会找到一个更好的家园，而有很大的机会找到一个更糟糕的家园。

Risk aversion may be an important strategy in evolutionary systems, since a single failure of a species to reproduce will prune its branch off the evolutionary tree. You are the result of a very long chain of successful matings going all the way back to the origin of life. One broken link in this chain and you would not be here. Of course, there is a difference between you not being here and Homo sapiens going extinct, but the general idea still holds. An evolutionary strategy that relies on gambles versus sure things is, literally, quite risky. Under some circumstances, playing the odds could potentially make sense, but the huge cost of failure—extinctions, like diamonds, are forever—may restrict such a strategy to very particular conditions. Often, slow and steady wins the evolutionary race. In the case of a honeybee hive, there is a tremendous investment involved in cleaving the hive. Given this, evolutionary success comes from finding a reasonable home for sure rather than taking a gamble that gives the bees a small chance of a much better home and a large chance of a much worse one.

蜜蜂并不是唯一一个拥有分散决策过程的物种。有些蚂蚁也有类似的寻找新家的方法。当这些蚂蚁群决定搬迁时，它会派出侦察兵寻找新的可能性。侦察兵调查完可能的地点后返回原群招募新蚂蚁的速度与新地点的质量有关——质量更好的地点会使侦察兵返回得更快。

Honeybees are not unique in having a decentralized decision-making process. Some species of ants have a related approach to finding new homes. When a colony of these ants decides to move, it sends out scouts to search for new possibilities. The speed at which scouts that have investigated a possible site return to the original colony to recruit new ants is tied to the quality of the new site—better-quality sites cause the scouts to return faster.

当侦察蚁返回原先的蚁群时，它会通过一种称为“并排奔跑”的过程，教另一只蚂蚁回到新家的路。并排奔跑需要对新成员进行繁琐的训练，但它的优点是新成员可以沿途学习所需的地标，以便它也能返回原先的蚁群并教给其他成员。就像蜜蜂一样，当在新地点形成群体时，行为就会发生变化。与使用并排奔跑相比，返回原家的蚂蚁只需带上它们的巢穴同伴并将它们带到新家。携带的优点是它比并排奔跑快三倍。缺点是它不允许新成员学习路径，但是一旦选择了新巢穴，就不需要这样的知识了。

When a scout returns to the original colony, it teaches another ant the way back to the new home by a process called tandem running. Tandem running requires the tedious training of the recruit, but it has the advantage that the recruit learns the needed landmarks along the way so that it too can return to the original colony and teach others. Like the bees, when a quorum forms at the new site, there is a change in behavior. Rather than using tandem running, the ants returning to the original home just pick up their nestmates and carry them to the new home. The advantage of carrying is that it is about three times faster than tandem running. The disadvantage is that it doesn’t allow the new recruits to learn the path, but such knowledge is not needed once the new nest is chosen.

我们是否看到人类系统中形成了蜂巢式思维？也许吧。回想一下Billboard音乐排行榜的类比。随着歌曲被发现，它们被播放得更频繁。随着它们被播放得更频繁，听到它们的人也越来越多，如果他们喜欢它们，他们也会开始播放这首歌（或者更有可能收听播放这首歌更频繁的电台）。随着时间的推移，最受欢迎的歌曲会升到榜首，并且通常会在那里停留很长时间。低质量的歌曲无法吸引新的听众，并从排行榜上掉下来，再也不会被听到。

Do we see hivelike minds forming in human systems? Perhaps. Think back to the analogy to the Billboard music charts. As songs get discovered, they get played more often. As they get played more often, more people hear them, and if they like them, they start to play the song as well (or, more likely, listen to stations that play the song more often). Over time, the most popular songs rise to the top and can often remain there for long periods of time. Low-quality songs fail to recruit new listeners and fall off the charts, never to be heard again.

消费品（例如 MP3 播放器和智能手机）可能遵循类似的过程。在这些市场刚起步时，早期采用者的消费者会随心所欲地出去购买。每次这些采用者使用产品时，他们实际上都在为蜂群中的其他成员表演摇摆舞。产品越好，他们就越有可能使用它，也就是说，跳舞的时间越长。随着新消费者进入市场，他们会观察其他消费者，而这些观察会影响他们自己的购买行为。请注意，拥有具有独特可观察特征的产品（想想 iPod 的白色耳机）在这里是一种优势（尤其是在这种情况下，因为产品的主要部分通常藏在口袋里）。随着正反馈循环开始建立，我们经常会看到一种产品起飞并开始主导市场。

Consumer goods, such as MP3 players and smartphones, may follow similar processes. At the start of these markets, early-adopting consumers go out and buy on a whim. Every time these adopters use the product, they are essentially performing a waggle dance for the other members of the hive. The better the product, the more likely they are to use it—that is, the longer the dance. As new consumers enter the market, they observe others, and those observations influence their own purchasing behavior. Note that having a product with distinctive observable features (think of the iPod’s white earbuds) is an advantage here (and especially in this case, since the main bulk of the product is usually hidden away in a pocket). As the positive feedback loops begin to mount, we often see one product take off and begin to dominate the market.

人类社会系统经历蜂巢式过程的另一个例子是政治竞争。在初选中，我们有许多候选人争夺认可。候选人从捐款中获得支持，并从潜在选民那里获得忠诚，这些选民出现在集会上，向他们的朋友和邻居宣传候选人。当然，也有辩论等论坛，候选人可以接触到大量公民，但即使在这些活动中，观众的支持（例如掌声）或主持人的支持（通过向领先者提出更多问题）也会影响观点其他人。在这些竞选的早期阶段，随着政治命运的起起落落，领跑者来了又去。但随着时间的推移，一个明显的领跑者出现了，提名也变得稳固了。（这个人是否代表了最好的人选，这个问题留到下次再说。）

Another example of human social systems undergoing hivelike processes arises in political contests. In primary races, we have numerous candidates vying for recognition. Candidates get their buzz from contributions and the loyalty that they engender from potential voters who show up at rallies and promote the candidate to their friends and neighbors. Of course, there are forums such as debates, where candidates get exposed to large swaths of the citizenry, but even during these events support from the audience (via, for example, applause) or from the moderator (by asking more questions of the front-runners) influences the views of others. In the early stages of these races, front-runners come and go as political fortunes rise and fall. Over time, though, a clear front-runner emerges and the nomination becomes solidified. (I’ll leave the question of whether this person represents the best of the bunch for another time.)

虽然这些例子集中于大规模的社会选择，但我们可以采取同样的想法，并反省我们每个人所做的选择。

While these examples focus on large-scale social choices, we can take the same ideas and look inward to the choices that each of us makes.

当我们考虑蜜蜂蜂巢时，我们忽略了这样一个事实：每只侦察蜂的行为都是由一个拥有大约 100 万个神经元的大脑控制的（相比之下，蚂蚁有 10 万到 25 万个神经元，而我们有大约 110 亿个神经元）。相反，我们抽象出了每只蜜蜂的行为由一组神经元控制的问题，只是将每只蜜蜂视为遵循一些简单规则的粒子。通过这样做，我们能够深入了解整个蜂群的行为。

When we considered the honeybee hive, we ignored the fact that the behavior of each scout bee was directed by a brain with around 1 million neurons (by comparison, ants have from 100,000 to 250,000 neurons, and we have around 11 billion). Instead, we abstracted away the issue of each bee’s behavior being controlled by a bunch of neurons and just considered each bee as being a particle following some simple rules. By doing so, we were able to gain insight into the behavior of the swarm as a whole.

复杂系统研究的一个特点是，系统在某一层次的行为细节，比如蜜蜂大脑中的神经元，可以在另一个层次上抽象地处理，比如，通过引入假设，即个体蜜蜂遵循简单的规则，而不管这些规则是如何产生的。通过进行这样的抽象，我们可以将研究重点放在当前的行为层次上，在上述情况下，即个体蜜蜂之间的相互作用如何使蜂群能够做出统一的迁徙选择。当我们进行这种抽象之旅并向上或向下移动一个层次时，我们可以（我们希望）将我们在一个层次上发现的相同一般原则应用到另一个层次。也许相互作用的原子产生分子行为、相互作用的分子产生化学行为、相互作用的化学物质产生神经元行为、相互作用的神经元产生个体行为、相互作用的个体产生群体行为以及相互作用的群体产生生态系统行为的方式都受类似原则的支配。

One of the hallmarks of the study of complex systems is that the particulars of the system’s behavior at one level, say, the neurons in a honeybee’s brain, can be treated abstractly at another level, say, by introducing the assumption that individual bees follow simple rules, regardless of how such rules are generated. By making such abstractions, we can then focus our investigation on the current level of behavior, which in the above case is how interactions of individual honeybees allow the swarm to make a unified choice about where to relocate. When we take this journey of abstraction and move either up or down a level, we can (we hope) apply the same general principles we’ve uncovered at one level to another. Perhaps the ways that interacting atoms create molecular behavior, interacting molecules create chemical behavior, interacting chemicals create neuron behavior, interacting neurons create individual behavior, interacting individuals create colony behavior, and interacting colonies create ecosystem behavior are all governed by similar principles.

如果我们足够幸运，一个层面的见解将无缝地融入我们对另一个层面发生的事情的理解中。这提供了这样的可能性：这些系统之间存在着深刻的相似性。如果是这样，也许我们从研究蜜蜂分散的相互作用如何导致群体选择中获得的见解可以用来理解其他系统的选择行为。也许我们已经找到了一种简单的方法来理解从蜜蜂到大脑的选择。

If we are lucky, insights from one level will seamlessly flow into our understanding of what happens at another level. This offers the possibility that there is a deep similarity among such systems. If so, maybe the insights we gained from studying how the decentralized interactions of honeybees result in swarm choice can be used to understand the choice behavior of other systems. Perhaps we have come upon a simple way of understanding choice making ranging from bees to brains.

观察一群蜜蜂的一个好处是，我们可以看到所有的蜜蜂，并追踪它们各自的运动。当然，即使在这种情况下，这样做也并非易事，因为你必须标记和追踪数千只蜜蜂，但这仍然比追踪构成大脑的数十亿个神经元要容易。虽然我们无法追踪数十亿个神经元，但我们可以将极细的探针插入大脑并观察单个神经元的活动。通过许多这样的观察，我们开始了解单个神经元的行为如何导致集体决策。

One advantage of observing a swarm of honeybees is that we can see all of the honeybees and track their individual movements. Of course, even in this case doing so is not trivial, as you have to label and track thousands of honeybees, but it’s still easier than tracking the billions of neurons that can make up a brain. While we can’t track billions of neurons, we can insert extremely thin probes into a brain and observe the activity of a single neuron. From many such observations, we begin to understand how the behavior of individual neurons results in a collective decision.

William Newsome 和他的同事一直在使用这种技术来分析猕猴如何做出决策。例如，他们向一只猴子展示一个屏幕上随机放置的移动点，这些点中有一定比例的点全部向左或向右移动。训练猴子判断大多数连贯的点是向左移动还是向右移动，并通过将眼睛移到屏幕上的特定位置来指示这一决定。

William Newsome and his colleagues have been using this technique to analyze how macaque monkeys make decisions. For example, they present a monkey with a screen of randomly placed and moving dots, with some set proportion of these dots all moving either to the left or to the right. The monkey is trained to decide whether the majority of the coherent dots are moving left or right and to indicate this decision by moving its eyes to a particular spot on the screen.

这样的决定是可能的，因为哺乳动物大脑的视觉皮层中存在高度特化的神经元，它们可以检测所看到事物的一些非常特殊的特征。例如，某些神经元仅在眼睛看到水平边缘时才会激活。其他神经元专门检测特定方向的运动。这些运动检测神经元的激活是纽瑟姆猴子做出决定的关键感官输入。回想一下，只有一部分点在连贯地移动，因此来自这些神经元的输入信号相当嘈杂。在大脑的另一个区域，另一组神经元开始权衡传入的感官证据。这些神经元跟踪左偏向运动神经元与右偏向运动神经元相比在一段时间内激活的程度，当观察到的两个方向之一的激活总量开始占主导地位时，就会做出决定。当屏幕上的许多点都朝同一方向移动时，决策很容易、快速且无错误。当信号更加混乱，比如当只有一小部分连贯的点时，决策需要更多时间并且准确性更低。

Such a decision is possible because within the visual cortex of a mammal’s brain are highly specialized neurons that can detect some remarkably specific features of what is being viewed. For example, certain neurons fire only when the eye sees, say, a horizontal edge. Other neurons specialize in detecting motion in a specific direction. It is the firing of these motion-detecting neurons that is the crucial sensory input into the decision that Newsome’s monkeys were making. Recall that only a proportion of the dots are moving coherently, so the input signals from these neurons are rather noisy. In another area of the brain, a different set of neurons begins to weigh the incoming sensory evidence. These neurons track how much the left-favoring motion neurons are firing over time compared to the right-favoring motion neurons, and when the total amount of observed firing in one of the two directions begins to dominate, a decision is made. When a lot of the dots on the screen are moving in the same direction, the decision is easy, quick, and free of error. When the signals are more mixed, such as when there is only a small proportion of coherent dots, the decision takes more time and is less accurate.

支持某一立场的证据不断积累，最终导致最终决策，这与我们在蜜蜂群中看到的情况类似。在这两个系统中，证据都是随着时间的推移慢慢积累的，直到证据变得如此强大，以至于做出最终决策。在蜜蜂系统中，正如我们所看到的，这个过程内置了保护措施，导致对看起来更好的选择进行更多测试。大脑是否有类似的东西并不明显，尽管放电神经元可能会萎缩或改变相关神经元的敏感性，从而导致类似的行为。即使没有这一点，乍一看似乎完全不同的系统之间的相似性也是令人信服的——蜜蜂和大脑可能密切相关。

The accumulation of evidence in support of one position or another, eventually leading to a final decision, is similar to what we see in honeybee swarms. In both systems, evidence is slowly accumulated over time to the point where it becomes so overwhelming that a final decision is made. In the honeybee system, as we have seen, safeguards are built into the process that result in more testing of the better-appearing choices. It is not immediately obvious that the brain has an analog to this, though it is possible that firing neurons might either atrophy or alter the sensitivity of related neurons, resulting in similar behavior. Even without this, the similarities between what might at first appear to be rather disparate systems is compelling—bees and brains may be closely related.

任何系统都无法保证最终决策是正确的。蜜蜂群可能会选择一个较差的蜂巢，这可能是因为最佳选择从一开始就没有被确定，或者因为在偶然事件中，它没有得到足够的强化，而较差的选择却能够获得足够的立足点，从而产生对它有利的正反馈。同样，大脑中的随机事件会导致运动神经元的放电模式产生足够的噪音，或导致决策神经元出现错误，从而扭转选择。猴子的决策正确率约为 95%51％的点移动连贯，而只有70％的点移动正确，而只有13％的点移动连贯。

There is no guarantee in any of these systems that the final decision will be the right one. It is possible for the honeybee swarm to choose an inferior hive, perhaps because the best option was never identified in the first place, or because, given chance events, it was not sufficiently reinforced while an inferior choice was able to get enough of a foothold that the positive feedback worked in its favor. Similarly, random events in the brain can cause enough noise in the firing patterns of the motion neurons or errors in the decision neurons to reverse the choice. The monkeys get about 95 percent of the decisions correct when 51 percent of the dots moved coherently and only 70 percent correct when 13 percent were coherent.

蜜蜂和大脑之间的机制相似性表明，也许可以建立跨系统的更深层次联系。许多看似智能的系统实际上可能是简单、相互作用的粒子的结果。我们知道，复杂系统擅长将相互作用的粒子组组合起来，形成更大规模的结构，而这些结构不属于任何粒子的意图或个体能力。因此，也许更大规模的结构表现出一些非凡的智能并不太令人惊讶。

The similarity of mechanisms between bees and brains suggests that perhaps a deeper connection across systems can be made. It may be that a lot of systems that seem intelligent are in fact the result of simple, interacting particles. We know that complex systems are adept at taking groups of interacting particles and forming larger-scale structures that are no part of any particle’s intention or individual ability. Thus, perhaps having larger-scale structures display some extraordinary intelligence is not too surprising.

蚁群和蜂群一样，必须做出各种决策，例如是否派出工蚁去寻找食物还是修复蚁丘等等。黛博拉·戈登 (Deborah Gordon) 和其他人发现，当蚂蚁决定做什么时，它会受到其他蚂蚁行为的影响。如果一只蚂蚁遇到很多其他蚂蚁带着食物回来，它也会出去采集食物。如果食物充足，它很容易找到，蚂蚁会更快地带着食物回来。这会鼓励其他蚂蚁也去寻找食物。如果食物稀缺或周围有捕食者，很少有蚂蚁会带着食物回来，工蚁会去做其他任务。无论是哪种情况，“做其他蚂蚁正在做的事情”的规则都会导致蚁群的生产行为。

An ant colony, like a bee colony, has to make a variety of decisions, such as whether to send out workers to find food versus repairing the mound and so on. Deborah Gordon and others have found that when an ant decides what to do, it is influenced by the actions of other ants. If an ant encounters a lot of other ants returning with food, she too will go out and gather food. If food is plentiful, it will be easy to find and ants will return faster with food. That will encourage other ants to seek food as well. If food is scarce or if there is a predator about, few ants will return with food, and workers will do other tasks. In either case, the rule that says “Do what other ants are doing” leads to productive behavior for the colony.

这并不是说盲目遵循规则总是最佳的。例如，行军蚁会遵循其他蚂蚁发出的化学信号。这种行为通常是适应性的，因为它将成千上万只蚂蚁的行动组织成这种阵型适合快速移动蚁群或捕猎，仅基于局部信号，无需全局指示。不幸的是，这种策略有时会失败，当一队军蚁无意中开始追随自己的踪迹时，形成一个圆形的磨坊（见图 7.5），随着时间的推移，所有参与者都会遭遇不幸。

That is not to say that blindly following a rule will always be optimal. For example, army ants follow the chemical signals laid by others. This behavior is usually adaptive, as it organizes the actions of tens of thousands of ants into formations suitable for quickly moving the colony or hunting prey, based only on local signals and without the need for global directions. Unfortunately, such a strategy can sometimes fail when a line of army ants inadvertently begins to follow its own trail, forming a circular mill (see Figure 7.5) that, with time, ends badly for all involved.

图 7.5：当控制每只蚂蚁行为的简单规则（即跟随其他蚂蚁留下的信息素踪迹）出现偏差，它们会意外地开始追踪自己时，就会形成一个圆形蚂蚁磨坊。几天之内，被困在磨坊中的蚂蚁就会死亡。

Figure 7.5: A circular mill of ants forms when the simple rule governing each ant’s behavior—namely, follow the pheromone trail left by other ants—goes awry, and they accidentally begin to track themselves. Within a couple of days, ants caught in the mill will perish.

全局行为是任何一组相互作用的粒子的必然结果。有时这种行为是混乱、无序的，难以理解，就像你周围的空气分子一样，像游泳池一样相互碰撞球——尽管即使在这种系统中也存在一种平均行为，即以良好的可靠性将分子大致均匀地分布在房间各处，而不是将它们全部集中在一个角落。（后一种行为是可能的，但可能性不大。）在其他时候，局部相互作用会导致看起来更有组织、更连贯的整体行为。没有人能保证这种有组织的行为是有成效和有用的，尽管我们确实有这样的例子。军蚁可以形成 60 英尺宽、3 英尺厚的阵线，像推土机铲刀一样穿过森林寻找猎物。蜜蜂群会做出生死攸关的决定，决定将成千上万只蜜蜂重新安置到哪里。神经元感知外界并制定有用的决策，决定采取什么行动。

Global behavior is the necessary result of any set of interacting particles. Sometimes this behavior is chaotic, disorganized, and hard to fathom, as in the molecules of air that surround you, bumping off one another like pool balls—although even in this kind of system there is an average behavior that, with good reliability, distributes molecules roughly evenly about the room instead of having them all concentrated in one corner. (This latter behavior is possible, though not very likely.) At other times, local interactions result in global behavior that appears far more organized and coherent. There is no guarantee that such organized behavior is productive and useful, though we do have examples where this is so. Army ants can form sixty-foot-wide, three-foot-thick fronts that go through the forest seeking prey like a bulldozer blade. Honeybee swarms make life-and-death decisions about where to relocate tens of thousands of bees. Neurons sense the outside world and formulate useful decisions about what action to take.

这种富有成效的自组织系统可以通过进化力量来磨练。虽然物理定律可能是固定的，但这些定律发挥作用的内部化学环境却不是。因此，通过重组一种或另一种分子汤，可以调用不同的规则，如果一组特定的规则导致全球行动导致某种更高的目的，进化就可以为后代捕捉这些条件。因此，进化力量可以形成依赖复杂分子相互作用的生物体，这些相互作用允许个体和超生物进行新陈代谢、信息处理、繁殖，甚至深思熟虑的决策。

Such productive, self-organizing systems can be honed by evolutionary forces. While the laws of physics may be fixed, the internal chemical environments in which these play out are not. Thus, by recombining molecular soups of one type or another, different rules can be invoked, and if a particular set of rules results in global actions that lead to some higher purpose, evolution can capture these conditions for future generations. As a result, evolutionary forces can form organisms relying on complex molecular interactions that allow metabolisms, information processing, reproduction, and even thoughtful decision making by individuals and superorganisms.

此类系统可以不断演化，但人类也可以创造和完善它们。拍卖市场中出现了一个有趣的案例，即人类衍生的局部规则被设计用于产生富有成效的全球性成果。拍卖由每一位参与者都必须遵守的简单规则集组成。这里显然的目标是找到一些规则集，这些规则集即使对于自私自利的个人，也会导致一系列具有一些良好全球特性的交易，例如确保参与者在拍卖期间做出最有利可图的交易。

Much as such systems can evolve, they can also be created and honed by humans. An interesting case of human-­derived, local rules being designed for productive global outcomes arises in auction markets. Auctions are composed of simple sets of rules that every participant must obey. The obvious goal here is to find sets of rules that, even with self-interested individuals, will result in a sequence of trades that has some nice global properties, such as ensuring that the most profitable deals possible are made by the participants during the auction.

有记录的最早拍卖发生在公元前 500 年左右的巴比伦。当时，女性被拍卖以结婚，最理想的妻子的销售收入被用来补贴那些不太理想的妻子的交易。这种机制在 20 世纪 90 年代的“费用回扣”制度讨论中再次出现。在这些拍卖中，对低效技术（如耗油卡车）征收的费用被用来资助补贴购买更节能的车辆的回扣。

The earliest auction on record is from around 500 B.C. in Babylon. Women were auctioned off for marriage, with the revenue acquired from the sale of the most desirable wives being used to subsidize the trades of the less desirable wives. Such a mechanism reemerged in the 1990s in discussions of “feebate” systems. In these auctions, fees imposed on less-efficient technologies, such as a gas-guzzling truck, are used to fund rebates that subsidize the purchase of more energy-efficient vehicles.

自巴比伦时代以来，人们已经开发出数百种不同的拍卖机制，但只有少数几种被广泛使用。大多数人一想到拍卖，就会想到公开叫价的英式拍卖。这种拍卖的参与者不断提高出价，直到没有人愿意出更高的价，此时商品将以最后出价卖给最高出价者。在荷兰式拍卖中——荷兰过去每天早上出售大量新鲜切花等商品——价格一开始远高于人们愿意为该商品支付的价格。然后价格降低，直到买家同意接受所提供的批次。一些拍卖，如金融市场中常用的拍卖，结合了英式拍卖和荷兰式拍卖的特点，潜在买家不断提高购买报价（出价），而潜在卖家不断降低销售报价（要价），直到有人同意接受当前可用的报价之一。其他拍卖机制以有趣的方式改变规则。例如，在第二价格拍卖或维克里拍卖中，潜在买家秘密提交出价，出价最高的人赢得拍卖——但她支付的价格是由第二高出价决定的，而不是她自己的。维克里拍卖的一种变体每周用于出售价值数十亿美元的美国国库券。

Since Babylonian times, hundreds of different auction mechanisms have been developed, though only a few types are widely used. When most people think of an auction, it is the open-outcry English auction that comes to mind. Participants in this auction increase the bid until no one wants to bid any higher, at which point the good is sold to the highest bidder at the last price bid. In a Dutch auction—used to sell, among other goods, large quantities of freshly cut flowers each morning in Holland—prices start out well above what anyone would want to pay for the good. The price is then lowered until a buyer agrees to take the offered lot. Some auctions, like those commonly used in financial markets, combine features of both English and Dutch auctions, with potential buyers making ever-­increasing offers to buy (bids) while potential sellers make ever-decreasing offers to sell (asks) until someone agrees to accept one of the currently available offers. Other auction mechanisms alter the rules in interesting ways. For example, in a second-price or Vickery auction, the potential buyers covertly submit their bids, and the highest bidder wins the auction—but the price she pays is determined by the second-highest bid instead of her own. A variant of the Vickery auction is used to sell billions of dollars’ worth of United States Treasury bills each week.

拍卖规则是由人类的聪明才智和贪婪以及历史的考验所创造的，它与蜜蜂群体中出现的行为基因非常相似。个人通过这些规则进行互动，创造出可能与已实施的规则甚至任何个人的目标脱节的全球行为。一些规则会导致不良后果，例如，买家或卖家能够相互勾结并利用对方，或者商品无法及时流通以实现最佳用途。与此类不良后果相关的拍卖机构往往会消亡。其他规则（如英国拍卖）会随着时间的推移而持续存在，因为买家和卖家都发现参与其中的价值此类拍卖。此外，遵守这些规则的社会往往会繁荣发展。

The rules of an auction—created by the ingenuity and greed of man and the trials of history—are much like the behavioral genes that arise in the honeybee colony. Individuals, interacting through these rules, create global behavior that may be disconnected from the rules that have been imposed or even the goals of any individual. Some sets of rules lead to bad outcomes where, say, buyers or sellers are able to collude and take advantage of one another, or goods do not flow in a timely manner to their best use. Auction institutions associated with such bad outcomes tend to die out. Other rules, such as the English auction, persist over time, as both buyers and sellers find value in participating in such auctions. Moreover, societies that embrace these rules tend to thrive.

拍卖只是人类社会系统如何采用一套简单的规则来产生自发和富有成效的社会秩序的一个例子。当然，还有许多其他例子。《罗伯特议事规则》（1876 年首次出版）以议会和立法机构使用的规则为蓝本，目的是指导群体中个人的互动，从而产生富有成效的群体层面的决策。同样，宪法、法律规则、法院和国际条约都是出于对新兴智慧的希望，尽管即使是最完善的规则有时也会导致循环往复。

Auctions are just one example of how a human social system can adopt a set of simple rules designed to generate spontaneous and productive social order. Of course, many other examples exist. Robert’s Rules of Order (first published in 1876) was modeled on the rules being used in parliaments and legislative houses, with the goal of directing the interactions of individuals in groups in a way that would result in the emergence of productive, group-level decisions. Similarly, constitutions, rules of law, courts, and international treaties are all derived in the hope of emergent wisdom, though even the best-laid rules can lead to a circular mill at times.

复杂系统理论尚处于起步阶段。我们知道可能有许多规则集会导致类似的涌现特性，因此人们可能怀疑这也适用于上述类型的系统。以民主制度的概念为例。自希腊城邦时代以来——大约与巴比伦拍卖同时——人们尝试了各种各样的民主规则。它们在赋予每个公民的代表权和自由度方面往往各不相同，但所有这些规则都表现出类似的民主意识。

The theory of complex systems is still in its infancy. We know that there may be many sets of rules that lead to similar emergent properties, and thus one might suspect that this is also true for the types of systems discussed above. Take, for example, the notion of a democratic system. Since the time of the Greek city-states—at roughly the same time as the Babylonian auctions—a variety of democratic rules have been tried. They often differ from one another in the amount of representation and freedom given each citizen, yet a similar sense of democracy emerges from all of them.

或者，考虑宗教体系中包含的各种信条，它们都试图唤起一套能够产生富有成效的社会的信念。不同的宗教试图以不同的方式唤起这些信念，甚至在一个宗教中也是如此。由于宗教分支的不同，十诫经常会有改进（喜剧演员乔治卡林可以将十诫简化为两条：“你必须永远诚实忠诚”和“你必须努力不杀死任何人”），但它们都可能导致类似的结果。

Alternatively, consider the various tenets contained in religious systems, all trying to invoke a set of beliefs that will result in a productive society. Different religions try to invoke such beliefs in different ways, and even within a given religious branch there are often refinements (comedian George Carlin was able to reduce the Ten Commandments down to just two: “Thou shall always be honest and faithful” and “Thou shall try really hard not to kill anyone”), yet they all may lead to similar outcomes.

拥有一个更好的新兴组织理论将带来很多实际好处，使我们能够制定或简化一系列规则，从而产生富有成效的结果。想想这种方法对我们的税法的价值。在美国，现行税法包含约 340 万个单词（相当于约 24 兆字节的数据）。这些单词创建了一套税收规则，无论好坏，这些规则都组织了我们社会的关键部分，包括政府支出、收入不平等、就业机会、工业生产、投资选择、政治倾向、逃税的可能性等等。当前系统的复杂性非常高，也许没有必要。新兴组织理论可能会指出一套大大简化的规则，可以产生更好的结果。

Having a better theory of emergent organization would have a lot of practical benefits, allowing us to generate or simplify sets of rules that will result in productive ends. Think about the value of such an approach for something like our tax code. In the United States, the current tax code contains around 3.4 million words (the equivalent of about twenty-four megabytes of data). These words create a set of tax rules that, for better or worse, organize key parts of our society, including government spending, income inequality, employment opportunities, industrial production, investment options, political affiliations, the likelihood of cheating on taxes, and on and on. The complexity of the current system is very high, and perhaps unnecessarily so. A theory of emergent organization might point to a vastly simplified set of rules that could produce better outcomes.

即使没有成熟的涌现理论，蜜蜂寻找新蜂巢位置等例子也可以提供一些有用的见解。进化使蜜蜂能够在不依赖集中信息或权威的情况下找到一个好的家。社会、政府、军事和商业领域也存在类似的问题，也许这些问题可以使用相关机制来解决。各种工程问题也可能得到解决对于这样的解决方案，基于蜜蜂的机制可用于创建分散的决策系统，收集和突出显示从基于网络的搜索到商业或国家安全情报收集等关键信息。

Even without a full-blown theory of emergence, examples such as honeybees searching for a new hive location may provide some useful insights. Evolution has enabled the honeybees to discover a good home without relying on centralized information or authority. Similar problems exist in social, government, military, and business domains, and perhaps these problems could be solved using related mechanisms. Various engineering problems may also be amenable to such solutions, and honeybee-based mechanisms could be used to, say, create decentralized decision systems that gather and highlight key information ranging from web-based searches to intelligence gathering for business or national security.

虽然试图修改莎士比亚的作品以使其符合科学准确性是徒劳的，但我们会尝试：“蜜蜂（以及大脑和社会）就是这样工作的，它们通过自然界的一条（简单）规则将（自组织）秩序的行为传授给一个由科学家和从业者组成的民族王国。”虽然语言的诗意因这些修改而受到严重损害，但科学的诗意却没有受到影响。在简单规则的支配下，相互作用的系统可以产生自发的、系统范围的行为，这些行为既是这些基本规则的一部分，又与它们完全脱节。这种魔法可以发生在我们世界的各个层面，从蜜蜂到大脑，甚至更远。

While trying to modify Shakespeare for scientific accuracy is a fool’s errand, nonetheless we’ll try: “For so work the honey-bees [and brains and societies], creatures that by a [simple] rule in nature teach the act of [self-organized] order to a peopled kingdom [of scientists and practitioners].” While the poetry of the language is seriously compromised by these modifications, the poetry of the science is not. Governed by simple rules, interacting systems can result in spontaneous, system-wide behavior that is both a part of those underling rules yet wholly disconnected from them. Such magic can, and does, happen at all levels of our world, from bees to brains and beyond.

八

eight

从草坪护理到种族隔离：网络

From Lawn Care to Racial Segregation: Networks

炫耀性地消费贵重物品是休闲绅士赢得声誉的一种手段。

Conspicuous consumption of valuable goods is a means of reputability to the gentleman of leisure.

—托尔斯坦·凡勃伦， 《有闲阶级论》

—Thorstein Veblen, Theory of the Leisure Class

一个任何复杂系统的核心都是一组相互作用的代理。如果我们追踪谁与谁互动，我们就可以发现代理之间的联系网络。毫不奇怪，这些网络的结构很重要，无论是从各种复杂系统中存在什么类型的网络来看，还是从不同的网络结构如何影响整个系统的行为来看。

At the heart of any complex system is a set of interacting agents. If we track who interacts with whom, we can uncover a network of connections among the agents. Not too surprisingly, the structure of these networks matters, both in terms of what types of networks exist across various complex systems and in terms of how different network structures influence system-wide behavior.

假设有一个湖泊，周围环绕着房屋。莱克兰的每栋房屋都在水面上，因此对于任何一栋房屋，其左侧和右侧都只有一个邻居。从鸟瞰图来看，每栋房屋都占据了湖边形成的圆圈上的一小块空间（见图 8.1）。

Consider a lake surrounded by houses. Each house in Lakeland is on the water, so for any given house there is only one neighbor to its left and one to its right. From a bird’s-eye view, each house occupies a bit of space on a circle formed by the lake’s edge (see Figure 8.1).

图 8.1：莱克兰社区。房屋围绕着湖泊排列，每户人家都与左侧和右侧的邻居相互交流。

Figure 8.1: The community of Lakeland. Houses are arrayed around a lake, with each household interacting with its immediate left- and right-side neighbors.

和大多数社区一样，每个居民的行为都会受到邻居的影响。举一个例子，假设每个居民必须决定在草坪上花多少精力——比如是否要修剪草坪。一个人在这里付出的努力可能取决于邻居的行为。如果邻居的草坪整洁如果岭，那么你可能也会这样做。如果邻居的草坪像杂草丛生的丛林，那么你的草坪护理工作可能会减少。

As in most neighborhoods, the behavior of each resident is influenced by her neighbors. To take just one example, suppose that each resident has to decide how much effort to spend on her lawn—say, whether to mow or not. The amount of effort that one exerts here may depend on the actions of one’s neighbors. If the neighbors keep immaculate, putting-green-like lawns, then you might be inclined to do so as well. If the neighboring lawns resemble weed-infested jungles, then your lawn care efforts might wane.

为了探索这个世界，我们假设每个星期天每个居民都会决定是否修剪草坪。这个决定受到她两个近邻（一个在左边，一个在右边）的强烈影响。为了简单起见，我们假设如果两个邻居都采取了与她上周相反的行动，那么她本周就会改变行动。否则她将继续做她上周做的事情。

To explore this world, let’s assume that every Sunday each resident decides whether to mow her lawn. This decision is strongly influenced by her two immediate neighbors (one to the left and one to the right). To keep things simple, we assume that if both neighbors took the action opposite of what she did last week, then she will alter her action this week. Otherwise she will continue to do what she did the prior week.

这种行为规则相当于一种粗略的多数原则。有三人（居民和她的两个邻居）“投票”决定该做什么。如果居民和她的至少一个邻居上周做了同样的事，那么这个多数决定决定了居民本周要做什么。相反，如果居民上周偏离了她的两个邻居，那么他们的两票将推翻她的票，她将改变自己的行为。

This rule of behavior is equivalent to a crude form of majority rule. There is a group of three (the resident and her two neighbors) that is “voting” on what to do. If the resident and at least one of her neighbors did the same action last week, then this majority decision dictates what the resident does this week. If, instead, the resident deviated from both of her neighbors last week, then their two votes overrule hers, and she alters her behavior.

我们已经具备了足够多的元素，可以开始探索莱克兰固有的系统范围行为。剩下的一个部分是草坪护理季节第一周会发生什么。上述行为是基于前一周的行为，显然季节开始时没有前一周。因此，为了初始化系统，我们将为每个居民掷硬币来确定她的初始行动。

We have almost enough elements in place to begin exploring the system-wide behavior inherent in Lakeland. The one remaining piece is what happens during the first week of the lawn care season. The behavior above is predicated on the previous week’s behavior, and obviously there is no previous week at the start of the season. So to initialize the system, we will flip a coin for each resident to determine her initial action.

乍一看，您可能会认为，在多数人原则下，第一周多数人做出的任何选择都将决定第二周的行为，莱克兰的每个人要么一直修剪草坪，要么从不修剪。虽然这看起来很直观，但请记住，每个居民的行为只与她近邻的行为有关，因此莱克兰所有人最初的多数人选择的整体信息不可能在第二周立即传递给每个居民。根据这一观察，您可能会修改最初的直觉，并想象随着时间的推移，随着邻居的影响，最初的多数人将慢慢地在湖边流动，最终经过几周后，系统最终会协调最初做出的任何多数人决定。唉，就像在大多数复杂系统中一样，这种明智的直觉是错误的。

At first glance you might think that, given majority rule, whatever choice is in the majority the first week will dictate the behavior for the second week, and everyone in Lakeland will either always mow their lawn or never mow it. While this seems intuitive, recall that the behavior of each resident is tied only to that of her immediate neighbors, so there is no way for the global information about the initial majority choice across everyone in Lakeland to be instantly transmitted to each resident during the second week. Given this observation, you might modify your initial intuitions and imagine that over time, as neighbor influences neighbor, the initial majority will slowly flow around the lake in such a way that the system eventually ends up, after a few extra weeks, coordinating on whatever majority decision was initially drawn. Alas, as in most complex systems, such sensible intuitions are wrong.

假设，无论出于什么原因，两个邻居开始采取相同的行动。如果发生这种情况，这两个居民中的每一位都会至少有一个直接邻居采取与她相同的行动。根据多数规则，这意味着这两个邻居将来都不会改变她的行动。

Suppose, for whatever reason, two next-door neighbors start to take the same action. If this occurs, each of these two residents will always have at least one immediate neighbor taking the same action that she is doing. Given majority rule, this implies that neither of these two neighbors will ever change her action in the future.

因此，只要两个邻居采取相同的行动，他们就会在本赛季的剩余时间里锁定在该行动上。由于这种锁定取决于这对邻居共同采取的行动，这表明，当我们观察系统时随着时间的推移，我们将看到邻居们形成岛屿，采取共同的行动（总是或从不割草）。

Thus, anytime two neighbors take the same action, they will lock themselves into that action for the rest of the season. Since this lock-in depends on the action that is common across the pair, it suggests that as we watch the system over time we will see the formation of islands of neighbors taking a common action (either always or never mowing).

目前，我们先关注其中一个岛屿的边缘。如果岛屿边缘附近的最近邻居决定采取与岛屿相同的行动，那么该邻居将成为岛屿的一部分，因为她将始终至少有一个邻居（岛屿上一个边缘的邻居）采取与她相同的行动，因此她将永远不会想在本赛季的剩余时间里改变她的行动。随着时间的推移，我们可能会看到各个岛屿在吸收采取类似行动的最近邻居的同时，慢慢地积累新成员。

For the moment, focus on the edge of one of these islands. If the nearest neighbor next to the island’s edge ever decides to take the same action as the island, then that neighbor becomes part of the island, since she will always have at least one neighbor (the one next to her on the previous edge of the island) taking the same action as she is, and hence she will never want to change her action for the rest of the season. Over time, we might see the various islands slowly accreting new members as they absorb like-actioned nearest neighbors.

因此，该系统动态的一部分是，当邻居发生相同的行为时，会建立一组孤立的共同行为岛。在季节开始时，这些岛屿将散布在圆圈周围，每个岛屿的确切位置和共同行为都与随机初始条件有关。一旦建立，这些岛屿可能会随着它们聚集类似行为的邻居而扩大规模。

Thus, part of the dynamics of this system is a set of isolated islands of common action being established as pairs of neighbors happen upon the same action. At the start of the season, these islands will be scattered about the circle, with the exact location of, and common action for, each island being tied to the random initial conditions. Once established, these islands are likely to grow in size as they accrete like-actioned neighbors.

这些不断扩大的岛屿是否会慢慢合并成一个包罗万象的岛屿，占据整个海岸线？要回答这个问题，请考虑当两个行为相反的岛屿相遇时会发生什么。在这些岛屿之间的边界，我们有两个最近的邻居采取不同的行动，但每个邻居都采取与另一边邻居相同的行动。因此，每个最近的邻居都有一个邻居（岛屿伙伴）采取相同的行动，另一个邻居（边界伙伴）采取相反的行动。鉴于多数规则，没有人愿意改变她选择的行动。因此，当两个行为相反的岛屿相遇时，它们都会在交汇点停止增长，并建立稳定的边界。

Do these growing islands slowly merge into a single, all-encompassing island that takes over the entire shoreline? To answer this question, think about what happens when two islands of opposite actions meet. At the boundary between these islands, we have two nearest neighbors taking different actions, but each one takes the same action as the neighbor on her other side. Thus, each of these nearest neighbors has one neighbor (the island mate) doing the same action and one neighbor (the boundary mate) doing the opposite. Given majority rule, neither one will want to change her chosen action. Thus, when two islands of opposite actions meet up, they both stop growing at the meeting point and a stable border is established.

鉴于上述情况，我们现在有足够的洞察力来了解 Lakeland 的动态。无论随机初始条件如何，我们都会看到共同行动的岛屿从岸边的那些地方出现，那里至少有两个最近的邻居碰巧采取了相同的行动。a这些岛屿中的每一个都将锁定让所有岛屿伙伴在本赛季的剩余时间内采取相同的行动，尽管这种共同行动在不同的岛屿上会有所不同。随着时间的推移，不属于任何现有岛屿的居民最终会聚集到一个岛屿中。当两个行动相反的岛屿相遇时，就会形成一个稳定的边界。这些过程最终使 Lakeland 处于稳定状态，其中相邻的居民群体都采取相同的行动，当我们绕圈从一个群体走到另一个群体时，这种行动会交替进行（见图 8.2）。

Given the above, we now have enough insights to understand the dynamics of Lakeland. Whatever the random initial conditions, we will see islands of common action emerging from those spots on the shore where at least two nearest neighbors happen to take the same action.a Each of these islands will lock into having all of the island mates taking the identical action for the rest of the season, though that common action will vary across the different islands. Over time, residents that are not part of any existing island eventually get accreted into an island. When two islands of opposite action meet, a stable boundary is formed. These processes eventually lead Lakeland to a stable state that has contiguous groups of residents all taking the same action, with that action alternating as we go from group to group around the circle (see Figure 8.2).

图 8.2： Lakeland 社区从随机的初始行动开始（左），基于多数规则发展（中），最终达到稳定的配置（右）。

Figure 8.2: The community of Lakeland begins with random initial actions (left), evolves based on majority rule (middle), and finally reaches a stable configuration (right).

因此，莱克兰会分裂成一组非常稳定的群体，它们会采取非常不同的行动，尽管所有居民都遵循相同的行为规则。此外，这些群体的形成与初始条件有关如果我们用新的初始条件重新运行该模型，我们可能会发现，上一季一丝不苟的草坪管理员在下一季会变成一个任由草坪枯萎的无赖。

Thus, Lakeland breaks down into a set of very stable groups pursuing very different actions, even though all of the residents follow the same behavioral rule. Moreover, the formation of these groups is tied to the initial conditions. If we rerun the model with new initial conditions, we might find that one season’s meticulous lawn keeper becomes next season’s cad letting her lawn go to seed.

当模型的见解可以应用于远远超出其最初动机的情况时，模型就会变得有价值。因此，即使关注莱克兰的草坪护理本身似乎并不有趣，但实际上有许多现象，如草坪护理、房屋维护以及你给房子外墙刷什么颜色，同样受到社会行为的影响，并且会影响从房产价值到社区长期稳定的一切。因此，一个基本的草坪护理模型可以让我们洞察社区如何分崩离析，甚至可能提出一些可能将它们重新组合在一起的政策——比如策略性地针对特定居民进行行为改变，这将对整个系统的状态产生巨大的积极影响。

Models become valuable when their insights can be applied to situations far beyond their initial motivation. So even if focusing on lawn care in Lakeland doesn’t seem of interest in and of itself, there are in fact a number of phenomena, such as lawn care, home maintenance, and what color you paint the exterior of your house, that are similarly influenced by social behavior and that can affect everything from property values to the long-term stability of a neighborhood. Thus, a basic model of lawn care can give us insights into how neighborhoods can fall apart, and perhaps even suggest policies that might put them back together—such as strategically targeting particular residents for behavioral changes that will result in large positive impacts on the overall state of the system.

邻居还可能影响各种其他社会行为。以教育为例。做作业（而不是参加聚会）、参加课堂讨论甚至上大学的愿望往往受到朋友行为的影响，因此类似莱克兰的模型可能会提供一些见解。类似的力量也可能影响犯罪行为，因为邻居的行为可能会鼓励或阻止犯罪活动，从贩毒到加入帮派。事实上，在某些社区，忽视草坪被视为一种犯罪行为，充其量是反社会的，甚至是非法的。

A variety of other social behaviors may be influenced by neighbors. Consider education. The desire to do your homework (rather than go to a party), participate in class discussions, or even go to college is often influenced by the actions of your friends, and thus a Lakeland-like model may offer insight. Similar forces may influence criminal behavior, as the actions of one’s neighbors may encourage or discourage criminal activities, ranging from selling drugs to joining gangs. Indeed, in some communities, ignoring your lawn is viewed as an offense that is at best antisocial and perhaps even illegal.

另一组明显的类似莱克兰模型可能涉及宗教和政治选择。宗教习俗，从庆祝特定节日到用灯光装饰房屋，再到宗教本身的选择，往往受到社交网络和个人顺从意愿的影响。同样，对政治问题的看法和政党的选择也会受到社交网络的影响。

Another obvious set of Lakeland-like models might involve religious and political choices. Religious practices, from celebrating particular holidays to decorating your house in lights to the choice of a religion itself, are often influenced by social networks and one’s desire to conform. Similarly, views on political issues and choice of political party can be influenced by social networks.

在莱克兰，我们假设每个人都生活在一个圈子里，社会影响只来自最近的邻居。这是一个非常极端和稀疏的社会网络，在更现实的模型中，我们可能会纳入更复杂的网络。例如，即使在莱克兰，居民可能不仅受到最近邻居的影响不仅如此，它们还受到其次近邻的影响。此外，它们也许能看到湖对岸的情况，因此更远的邻居的行为也可能会产生影响。

In Lakeland, we assumed that everyone lived on a circle, and that social influences came only from one’s nearest neighbors. This is a very extreme and sparse social network, and in more realistic models we might incorporate more complicated networks. For example, even in Lakeland, residents might be influenced not only by their nearest neighbors but also by their next-nearest neighbors. Furthermore, perhaps they can see across the lake, so the actions of more remote neighbors might be influential as well.

我们发现，网络结构的变化通常会对整个系统的行为产生重大影响。考虑通过您认识的人将消息转发给您不认识的人的问题。假设您想向网络中随机选择的人发送一条消息，并且您只能将此消息传递给与您有直接联系的人，而该人又必须将其传递给她有直接联系的人，依此类推，直到消息到达目的地。您建立所需连接所需的最少链接数（平均）是多少？

It has been found that changes to the structure of a network often have a big influence on system-wide behavior. Consider the problem of relaying a message to someone you don’t know via people you do know. Suppose that you want to send a message to a randomly chosen person in the network and that you are only allowed to pass this message to someone you are directly connected to, who in turn must pass it to someone she is directly connected to, and so on, until the message arrives at its destination. What is the smallest number of links (on average) that it will take for you to make the needed connection?

在莱克兰，每个人都生活在一个圆圈里，只和她的近邻保持联系，随机选择的接收者很可能在圆圈的某个方向与原始发送者相距四分之一处（最多，接收者和发送者可以正好在彼此的对面，也就是一半的距离，所以平均而言，他们会在四分之一处）。由于消息只能通过网络中的链接流动，到达目标的最直接路线是发送者将消息传递给距离目标最短方向的最近邻居。邻居也会这样做，依此类推。因此，消息在到达目标之前，平均要经过莱克兰四分之一的人口。请注意，随着人口的增加，传递时间会更长将信息传递给目标所需的时间呈线性增长。如果湖周围有 60 亿人，则平均需要 15 亿步才能传递信息。

In Lakeland, where everyone lives on a circle and is only connected to her immediate neighbors, a randomly chosen recipient is likely to be one-quarter of the way around the circle from the original sender in one direction or the other (at most, the recipient and sender can be directly opposite each other, which is halfway around, so on average they will be at the one-quarter mark). Since messages can flow only across links in the network, the most direct route to the target will have the sender passing the message to her nearest neighbor in the shortest direction to the target. The neighbor will do the same, and so on. Therefore, the message will be passed through, on average, a quarter of the population of Lakeland before it arrives at the target. Note that as the population gets larger, the length of time to get the message to the target increases linearly. If there are 6 billion people arrayed around the lake, it will take, on average, 1.5 billion steps to deliver the message.

在莱克兰，每个人都只认识她最近的两个邻居。在实际网络中，虽然我们可能有很多非常本地的连接，但我们通常也有一些更远的连接。所以让我们修改一下莱克兰，让一些居民与随机选择的人建立联系。这个新网络就像我们原来的莱克兰，每个人仍然与他们最近的邻居保持联系，但增加了一些随机横跨湖面的新连接。这种新型网络（见图 8.3）被称为小世界网络，其原因稍后就会显现出来。

In Lakeland, everyone knows only her two nearest neighbors. In real networks, while we likely have a lot of very local connections, we often have a few more distant ones as well. So let’s modify Lakeland by giving some of the residents a connection to a randomly chosen person. This new network is like our original Lakeland, with everyone still connected to their nearest neighbors, but with the addition of a few new connections randomly spanning the lake. This new type of network (see Figure 8.3) is known as a small world network, for reasons that will become obvious in a moment.

图 8.3：通过采用 Lakeland 并添加一些随机的远距离连接而形成的小世界网络。此类连接的添加极大地改变了系统的消息传递动态。

Figure 8.3: A small world network formed by taking Lakeland and adding some random, distant connections. The addition of such connections dramatically alters the message-passing dynamics of the system.

在小世界中传递信息与我们最初在莱克兰所做的非常不同。在莱克兰，我们经历了从最近的邻居到最近的邻居的冗长过程，直到我们最终到达目标。在小世界中，您可以利用新的远程连接来加快信息的传递。小世界类似于地方道路和高速公路的网络。如果您想快速到达某个地方，您可以走几条地方道路上高速公路，一直走在高速公路上，直到您可以在目的地附近出口，然后沿着地方道路前往目的地。

Passing messages in a small world is very different from what we originally did in Lakeland. In Lakeland, we had the tedious process of going around the circle from nearest neighbor to nearest neighbor until we finally arrived at our target. In a small world, you can exploit the new, long-range connections to expedite delivery of the message. A small world resembles something akin to a network of local roads and highways. If you want to go somewhere fast, you take a few local roads to get on the highway, stay on the highway until you can exit near your destination, then proceed to your destination on the local roads.

虽然小世界网络显然应该加快信息传递速度（毕竟，它不能比以前采取更多的步骤，因为你总是可以恢复到外环，如果需要的话，我们可以使用最近邻方法），但令人惊讶的是，它所需的时间要少得多。以上面 60 亿居民为例，假设每个居民认识 30 个人，那么预期传递次数只有 6.6 左右——毕竟世界很小！回想一下，对于拥有 60 亿居民的 Lakeland，如果每个居民只有两个朋友，我们需要 15 亿步。如果我们假设有 30 个最近邻居，那么等效计算将需要在 Lakeland 传递一条消息 1 亿次。

While it is clear that small world networks should speed up message passing (after all, it can’t take any more steps than before, since you can always revert to the outer-ring, nearest-neighbor approach if need be), it is surprising how much less time it takes. Taking the example of 6 billion residents above, and assuming that each resident knows thirty people, then the expected number of passes is only about 6.6—it’s a small world after all! Recall that for a Lakeland with 6 billion residents we needed 1.5 billion steps if each resident had only two friends. If we assume thirty nearest neighbors, the equivalent calculation would require a message in Lakeland to be passed 100 million times.

因此，如果我们愿意接受小世界网络的假设，你和地球上其他人之间的分离度略大于六度（如果我们考虑到约十亿人因各种原因无法参与而损失的话）。小世界模型假设世界上任何两个人之间都可能存在随机联系，而这一假设可能不成立，因此将六度分离的估计值视为下限。无论如何，结果都是非凡的。

Thus, if we are willing to accept the assumptions of small world networks, there is a little more than six degrees of ­separation between you and someone else on the planet (if we allow for the loss of a billion or so folks given their inability to participate on various grounds). The small world model assumes that random connections are possible between any two people in the world, and this assumption may not hold, so consider the estimate of six degrees of separation as a lower bound. Regardless, the result is remarkable.

研究人员研究了各种网络，包括科学论文的合著者、Facebook 上的好友、构成我们电网的链接、控制基因表达的生物调节网络、简单大脑中神经元之间的连接以及网页之间的链接，仅举几例。越来越多的证据表明，这些网络中的许多网络具有深层的共同结构，这可能为开发一些关于此类网络如何产生和运作的统一理论奠定基础。

Researchers have investigated various networks, including coauthors of scientific papers, people who friend each other on Facebook, the links that make up our electric power grid, biological regulatory networks that control the expression of genes, the connections across neurons in simple brains, and links across web pages, to name just a few. The evidence is slowly accumulating that many of these networks have a deep common structure that may provide a basis for developing some unified theories of how such networks arise and behave.

1969 年，托马斯·谢林 (Thomas Schelling) 创建了一个有趣的模型，与上面讨论的模型类似。谢林对了解种族隔离问题很感兴趣。假设人们不是围着湖排成一排，而是每个居民占据棋盘上的一个方格（并非所有方格都被占据）。棋盘内部的每个居民都被八个相邻的方格包围。

In 1969 Thomas Schelling created an interesting model similar to the ones discussed above. Schelling was interested in understanding issues surrounding segregation. Instead of people arrayed around a lake, suppose that each resident occupies a square on a checkerboard (where not all of the squares are occupied). Each resident in the interior of the board is surrounded by eight neighboring squares.

假设每个居民都是X型或O型。我们假设这两种类型的居民彼此容忍，只要至少有30％的邻居与他们属于同一类型，他们就会乐意留在原地。但是，如果同类型邻居的比例低于30％，该居民将随机搬迁到其中一个空置的方格中。

Suppose that each resident is either a type X or O. We assume that the two types of residents are tolerant of each other and that as long as at least 30 percent of their neighbors are the same type as they are, they are content to stay in place. However, if the proportion of same-type neighbors drops below 30 percent, that resident will randomly relocate to one of the empty squares.

考虑到对拥有相同类型的邻居的偏好非常弱，人们可能期望该模型描述的世界会很快稳定下来，两种类型之间的隔离非常小。不幸的是，实际行为与这种预期相悖。

Given the very weak preference for having neighbors of the same type, one might expect that the world described by this model would quickly settle down to a state with very little segregation between the two types. Unfortunately, the actual behavior confounds such an expectation.

图 8.4 显示了居民在景观中随机排列的情况（顶部）和所有想要移动的人都移动后的情况（底部）。在模型开始时，由于居民是随机排列在棋盘上的，因此平均而言，50% 的居民邻居属于同一类型，50% 的邻居属于不同类型。如果您查看居民的初始配置，则几乎没有隔离的迹象——无论您感知到什么模式，都是因为您的大脑想要对随机性进行排序和模式化（这是一种常见现象——例如，硬币翻转的随机序列看起来更像是HTHHHTTH  ...... 而不是HTHTHTHT  ...... ）。

Figure 8.4 shows the arrangement of residents both randomly arrayed on the landscape (top) and after everyone who wants to move has done so (bottom). At the start of the model, since residents are randomly placed on the board, on average 50 percent of a resident’s neighbors are of the same type and 50 percent are different. If you look at the initial configuration of residents, there is little evidence of segregation—whatever patterns you perceive are due to your mind wanting to put order and pattern on the randomness (this is a common phenomenon—for example, random sequences of coin flips look far more like HTHHHTTH . . . than HTHTHTHT . . . ).

图 8.4： 360 个代理的谢林隔离模型，如果 30% 或更少的邻居属于同一类型，居民就会搬走。两种类型的居民由不同阴影的单元格表示，白色单元格表示无人居住。两个随机起始状态（顶部）都会导致下方对应的结束状态。在两次模型运行中，开始时相似类型邻居的可能性平均约为 50%，后来变成了相似类型邻居的可能性超过 70% 的隔离世界。（生成此输出的程序由 Robert Hanneman 创建。）

Figure 8.4: The Schelling segregation model with 360 agents, where residents move if 30 percent or fewer of their neighbors are of the same type. The two types of residents are shown by the differently shaded cells, with the white cells being unoccupied. Both random starting states (top) lead to the corresponding ending states directly below. In both runs of the model, what begins as a world where on average the likelihood of a similar-type neighbor is around 50 percent transforms into a segregated world with a greater than 70 percent likelihood of similar-type neighbors. (The program that generated this output was created by Robert Hanneman.)

从最初的起始条件来看，我们允许任何拥有 30% 或更少同类邻居的居民随机搬迁。如图所示，这样的过程很快就会导致大型、隔离的社区。事实上，我们发现，在系统稳定下来后，每个居民平均而言，ident 的邻居中大约有 70% 属于同一类型。因此，稍微倾向于至少有 30% 的邻居与您相似会导致 70% 的邻居与您相似。

From the initial starting conditions, we allow any resident who has 30 percent or fewer neighbors of the same type to randomly relocate. As can be seen in the figure, such a process quickly leads to large, segregated neighborhoods. Indeed, we find that after the system settles down, each resident, on average, has around 70 percent of her neighbors being of the same type. Thus, a slight preference for having at least 30 percent of your neighbors being like you leads to having 70 percent of your neighbors being like you.

你可能一开始会认为，我们用来初始化系统的随机混合足以让每个人都平均而言，每位居民的邻居中，有 50% 是同类。当然，50% 是总体平均值， 有些居民会住在同类居民比例较高或较低的社区中。因此，一些随机安置的居民会发现自己所处的社区同类型邻居数量不足，他们就会搬家。当一位居民搬家时，她的八个邻居中的每一位都会失去一位同类型的邻居，这可能足以打破一些老邻居同类型居民的平衡，促使他们也搬家。当社区中某一类型居民的比例远远超过 30% 时，它不仅会变得更加稳定，而且会驱逐相反的类型。与莱克兰发生的情况类似，连续的同类型居民岛的稳定配置开始形成，随着它们吸纳任何碰巧在附近定居的新流离失所的同类型居民，这些岛慢慢增长。

You might at first think that the random mixing we used to initialize the system would be sufficient to keep everyone in place, as on average each resident has 50 percent of her neighbors being similar. Of course, the 50 percent is an overall average, and some residents will live in neighborhoods with a higher or lower percentage of similar residents. Thus, some of the randomly placed residents will find themselves in neighborhoods with an insufficient number of same-type neighbors, and they will move. When a resident moves, each of her eight neighbors loses a neighbor of that type, and this may be sufficient to tip the balance of same-type residents for some of the old neighbors, inducing them to move as well. As the proportion of a given type of resident in a neighborhood goes well above 30 percent, it not only becomes more stable to that particular type but also drives out the opposite type. Similar to what happened in Lakeland, stable configurations of contiguous, same-type-­resident islands begin to form, and these slowly grow as they accrete any newly displaced, same-type residents that happen to land nearby.

我们之前已经看到过，正反馈回路如何使系统迅速进入远离起点的新自我强化配置。谢林系统受此类反馈回路控制。略微偏向于与同类邻居相处的代理会形成正反馈回路，同类相生。

We have seen before how positive feedback loops can cause a system to rapidly tip into a new, self-reinforcing configuration that is far away from its starting point. Schelling’s system is governed by such feedback loops. Agents with a slight preference to be with same-type neighbors form positive feedback loops, with like begetting like.

如果我们改变网络，我们可能会在系统中引发非常不同的行为。例如，谢林棋盘中出现的隔离程度往往会随着一些合理的替代网络配置而增加例如莱克兰的环路。总体而言，可以看出，这些隔离系统的关键驱动因素是任何特定居民与其邻居的邻居的重叠程度。

If we alter the networks, we may induce very different behavior in the system. For example, the degree of segregation that arises in Schelling’s checkerboard tends to increase with some reasonable alternative network configurations such as Lakeland’s loops. In general, it can be shown that the key driving factor in these segregation systems is the amount of overlap any given resident has with her neighbors’ neighbors.

在人类历史的初期，我们处于一个相当静态的网络中，由一个小部落内的一些密集联系以及偶尔与外界的联系组成，尽管这些联系往往是短暂的。随着时间的推移，随着我们发展出轻松移动和远距离通信的能力，这些网络变得更加密集和动态。在二十世纪，随着大众媒体的发展和一小部分人开始向其他人广播信息，社交网络变得更加紧密。

For the first part of human history, we were embedded in fairly static networks, consisting of some dense connections across a small tribe with occasional, though often transient, connections to outsiders. Over time, these networks have grown far more dense and dynamic as we have developed the ability to easily move and communicate across large distances. In the twentieth century, social networks grew more connected as mass media developed and a small group of people began to broadcast messages to others.

近来，随着计算机的出现，我们的网络变得更加复杂，因为我们与从未见过面、住在从未去过的地方的人成为“朋友”。现在，我们可以通过电子邮件、博客、状态更新和 144 个字符的消息与从几个忠实朋友到成千上万的追随者进行互动。我们发现自己处于由大量朋友、同事和其他各种联系人组成的重叠网络的交汇处。我们才刚刚开始了解这个新的超网络世界对复杂社会动态的影响。在 Facebook 上发布一张刚修剪过的草坪的照片可能会对您所在社区以外的人产生社会影响。

More recently, with the advent of computers, our networks have become even more complex, as we become “friends” with people we have never met in person who live in locations that we have never visited. We now interact with anywhere from a few dedicated friends to thousands of followers through email, blogs, status updates, and 144-character messages. We find ourselves at the nexus of overlapping networks consisting of large groups of friends, coworkers, and various other contacts. We are only beginning to understand the impact of this new, hypernetworked world in terms of complex social dynamics. Posting a picture of your freshly mowed lawn on Facebook may have social impacts far beyond your immediate neighborhood.

a有一种反常情况可能发生，即初始条件和代理数量使得我们在绕圈时动作完全交替。在这种情况下，每个居民都会在每个时间步骤切换自己的动作，系统永远不会稳定下来。随着系统规模的扩大，出现这种情况的可能性微乎其微。

a There is one perverse case that can occur when the initial conditions and number of agents are such that the actions perfectly alternate as we go around the circle. In this case, every resident will switch her action at each time step, and the system will never settle down. The likelihood of such a case arising is vanishingly small as the system increases in size.

九

nine

从心跳到城市规模：扩展

From Heartbeats to City Size: Scaling

“恶棍！”我尖叫道，“别再装模作样了！我承认了！——把木板撕碎！这儿，这儿！——那是他那可怕的心脏在跳动！”

“Villains!” I shrieked, “dissemble no more! I admit the deed!—tear up the planks! here, here!—it is the beating of his hideous heart!”

—埃德加·爱伦·坡，《泄密的心》

—Edgar Allan Poe, “The Tell-Tale Heart”

米动物的平均寿命约为 10 亿次心跳。无论体型大小，它们的生命都在随着每次心跳流逝。因此，一只平均心率约为每分钟 500 次的老鼠预计可以活 4 年。而平均心率每分钟 50 次的人类可以活 40 年左右。由于一生的心跳次数是固定的，基础心率越慢，寿命就越长。

Mammals live, on average, for roughly 1 billion heartbeats. No matter how large or small, their lives are ticking away with every beat. Thus, a mouse, with an average heart rate of about five hundred beats per minute, is expected to live for four years. A human, with fifty beats per minute, lives for around forty years. With a fixed number of lifetime heartbeats, the slower your base heart rate, the longer you live.

此类关系有助于预测甚至理解我们周围的世界。从老鼠到蓝鲸，以及介于两者之间的所有哺乳动物，我们现在只需知道动物的脉搏率，就可以对其寿命做出有用的预测。此外，心跳与其他生理特征有关，例如体重和代谢率，因此这些特征也可以预测。这种缩放关系的存在表明，这些系统背后可能存在一些更大的普遍规律。

Such relationships are useful for predicting, and perhaps even understanding, the world around us. From a mouse to a blue whale, and every mammal in between, we can now make a useful prediction about an animal’s life span knowing only its pulse rate. Moreover, heartbeat is tied to other physiological features, such as body mass and metabolic rate, so these too can be predicted. The existence of such scaling relationships suggests that there may be some greater, universal laws that underlie these systems.

从数学上讲，一个变量与另一个变量之间存在多种关系。两个变量可以具有线性关系，例如y = x。在各种系统中经常出现的一种特定类型的关系称为幂律。幂律表明，某事物的乘积等于另一事物的某个固定幂，例如y = x 2。例如，正方形的面积等于其边长的 2 次方（即，乘以自身两次）。如果我们将每条边的长度加倍，正方形的面积不会增加一倍，而是增加四倍（2 × 2 = 4）。立方体的体积等于其边长的 3 次方（乘以自身三次）。因此，将立方体的边长加倍，其体积就会增加八倍（2 × 2 × 2 = 8）。

Mathematically, there are many ways one variable could be related to another. Two variables could have a linear relationship, such as y = x. A specific type of relationship that arises regularly in a variety of systems is known as a power law. A power law states that something scales as something else raised to some fixed power, such as y = x2. For example, the area of a square is equal to the length of its side raised to the power of 2 (that is, multiplied by itself twice). If we double the length of each side, the square doesn’t double in area, it quadruples (2 × 2 = 4). The volume of a cube scales as the length of its side raised to the power of 3 (multiplied by itself thrice). Therefore, doubling the length of a cube’s sides results in eight times the volume (2 × 2 × 2 = 8).

这些几何关系似乎过于简单，无法解释复杂系统如何运作，但它们对生物学有一些有趣的启示。在一个大致呈立方体的动物世界里，当我们把它们的体型扩大一倍时，它们的表面积（比如皮肤的面积）会增加四倍，而它们的体积（比如内脏）会增加八倍。因此，单位体积的表面积会减少，这使得当你变大时更容易保持温暖（因为你通过皮肤散热，通过内脏产生热量）。这些几何关系还意味着，随着动物长大，它们的骨骼结构必须以不成比例的方式发生变化，因为骨骼支撑动物的能力（与骨骼的横截面或面积有关）只随着尺寸的平方而增长，而动物的重量（体积）则随着尺寸的立方而增长。后一种结果的好消息是，你看到的典型的 B 级电影中由笨手笨脚的清洁工在深夜实验室清洁期间撞倒了一桶放射性物质而引起的巨型动物袭击从一开始就注定要失败，因为这种生物相应大小的附肢会在其不成比例的重量下崩溃——大象有粗腿是有原因的。

These geometric relationships may seem too simple to shed much light on how complex systems work, but they have some interesting implications for biology. In a world of roughly cube-shaped animals, as we double their size their surface area (think amount of skin) goes up by a factor of four, while their volume (think guts) goes up by a factor of eight. Thus, there is less surface area per unit of volume, which makes it is easier to stay warm when you get bigger (since you lose heat through your skin and generate it via your guts). These geometric relationships also imply that as animals grow larger, their bone structure has to change in a disproportionate way, as the bones’ ability to support the animal (which is tied to the bones’ cross section or area) grows only as the square of size, while the weight of the animal (volume) grows as the cube. The good news of this latter result is that your typical B-movie attack of the giant whatever caused by a clumsy janitor knocking over a vat of radioactive whatnot during a late-night laboratory cleaning would be doomed from the start, as the creature’s proportionately sized appendages would collapse under its disproportionate weight—elephants have thick legs for a reason.

了解幂律中幂的值可以告诉我们系统如何缩放。如果幂为 1，那么当我们将独立变量（例如，一根棍子的长度）加倍时，我们只需将因变量（例如，棍子的重量）加倍。当幂大于 1 时，系统会超线性缩放，因此当我们将独立变量加倍时，因变量会增加一倍以上。这是我们在上面面积和体积关系中看到的缩放类型，其中幂分别为 2 和 3。最后，如果幂低于 1，系统会亚线性缩放，将独立变量加倍会导致因变量增加不到一倍。

Knowing the value of the power in a power law tells us how the system scales. If the power is 1, then as we double the independent variable (say, the length of a stick), we simply double the dependent one (say, the stick’s weight). When the power is greater than 1, the system scales superlinearly, so when we double the independent variable, the dependent variable more than doubles. This is the type of scaling we saw in the area and volume relationships above, where the powers were 2 and 3, respectively. Finally, if the power is below 1, the system scales sublinearly, and doubling the independent variable results in less than a doubling of the dependent variable.

异速生长是研究生物体物理特征和生理特征之间关系的学科。此类研究至少可以追溯到 1892 年奥托·斯内尔 (Otto Snell) 的工作。20 世纪 30 年代，马克斯·克莱伯 (Max Kleiber) 指出，动物的代谢率与其体重的 ¾ 次方成比例（即呈亚线性比例）。代谢率告诉我们生物体生存所需的能量。¾ 次方意味着我们只需要两倍的能量就能维持两倍半的体重。一般而言，这种关系意味着，随着动物体型变大，它们每单位体重所需的能量效率会更高。

Allometry is the study of relationships between the physical and physiological features of organisms. Such studies date back at least to Otto Snell’s work in 1892. In the 1930s, Max Kleiber noted that the metabolic rate of an animal scales to its mass raised to the ¾ power (that is, it scales sublinearly). The metabolic rate tells us the amount of energy needed for an organism to survive. A power of ¾ implies that we only need two times the energy to sustain two and a half times the mass. In general, this relationship implies that as animals get larger they are more efficient in the amount of energy needed per unit of mass.

由于新陈代谢与各种其他因素（如氧气摄入量和心率）息息相关，因此这些因素也存在缩放定律也就不足为奇了。呼吸和心率与质量成-¼ 次方缩放。请注意，如果我们在给定的寿命内呼吸或心跳次数固定，则意味着寿命与质量成¼ 次方缩放。在这种缩放下，如果您的体型是原来的十六倍，您的寿命将是原来的两倍。

Since metabolism is tied to all kinds of other factors, such as oxygen intake and heart rate, it is not surprising that scaling laws exists for these factors as well. Breathing and heart rates scale with mass to the −¼ power. Note that if we have a fixed number of breaths or heartbeats in a given life span, then this implies that life span scales with mass to the ¼ power. Under this type of scaling, if you are sixteen times as big, you will live twice as long.

掌握了异速生长定律后，我们现在能够预测一些关键结果，例如新陈代谢和寿命，而只需知道生物体的质量（见图 9.1）。虽然上面的许多例子都集中在哺乳动物身上，但你也可以将异速生长定律扩展到其他生物体。即使在极小的尺度上，例如单个细胞，它们仍然适用。因此，在地球上涵盖超过二十个数量级质量的广阔生命范围内，我们发现了一条将它们全部联系在一起的简单定律。

With allometric scaling laws in hand, we are now able to predict some critical outcomes—such as metabolism and life span—knowing only an organism’s mass (see Figure 9.1). While many of the examples above focused on mammals, you can extend the allometric scaling laws to other organisms as well. Even at extremely small scales, such as a single cell, they still hold. Thus, over a vast swath of life on earth encompassing more than twenty orders of magnitude of mass, we find a simple law that connects them all.

当出现这样的规律时，它表明了某种驱动整个系统的潜在机制。在代谢方面，杰弗里·韦斯特、吉姆·布朗和布莱恩·恩奎斯特已经发现了这种机制。这种机制背后的想法是，即使是像身体这样复杂的结构也会面临一些限制。这里的限制是对交换营养物质所需特征大小的物理限制，例如循环系统中的毛细血管。如果毛细血管可以变得有多小是有限制的，那么要想变大，你就需要找到一种方法将足够多的毛细血管塞进更大的空间，这样它们才能为组织供氧。这样的要求限制了整个系统。

When such laws appear, it suggests some underlying mechanism driving the entire system. In the case of metabolism, such a mechanism has been identified by Geoffrey West, Jim Brown, and Brian Enquist. The idea behind this mechanism is that even complex structures such as bodies face some constraints. Here, the constraint is on physical limits to the size of features required to exchange nutrients, such as the capillaries in your circulatory system. If there is a limit to how small capillaries can become, then to grow bigger you need to find a way to pack enough of them into the larger space so that they can oxygenate the tissues. Such a requirement constrains the whole system.

图 9.1：各种动物的代谢标度。两个轴都使用对数标度，因此根据幂律，绘制的点应全部落在一条线上。这里隐含的幂是 ¾，导致亚线性标度。这意味着随着生物体变大，它们的相对代谢需求会减少——一个两倍大的生物体需要的总代谢量不到两倍。（图片由 Geoffrey West 提供。）

Figure 9.1: Metabolic scaling across various animals. Both axes use logarithmic scales, and therefore under a power law the plotted points should all fall on a line. Here the implied power is ¾, leading to sublinear scaling. This implies that as organisms get larger their relative metabolic needs decrease—an organism twice as large needs less than two times the total metabolism. (Figure courtesy of Geoffrey West.)

想象一下，在炎热的天气里，一群口渴的人坐在体育场的一排座位上。假设过道上有一个小贩，他可以递给排在第一位的人一个杯子，如果她口渴，她要么喝掉杯子，要么把杯子传给下一个人，而下一个人也会采取同样的行为。这里的限制是小贩分发新杯子的能力和每个杯子的大小。如果排在座位上的人很少，水很容易满足每个人的口渴。然而，随着排在座位上的人数越来越多，如果每个人的喝水量都和以前一样，那么排在最后一排的人就永远喝不到水了。但如果每个人的口渴程度都减轻了——也就是说，如果我们降低每个人的新陈代谢——那么每个人的口渴程度都可以得到满足。为了维持更长的座位，我们需要不那么口渴的顾客。我们甚至可以量化他们应该少渴多少：在我们体育场的情况下，它是顾客数量的 1 倍（这使我们每个人的口渴程度的幂为 -1，总口渴程度的幂为 0）。因此，当我们增加第八个人时，如果每个人的口渴程度下降八分之一，现有的水量仍然足够。从我们的一维体育场转移到三维生物系统更加复杂，导致每人代谢的幂为 -¼质量单位和总代谢的¾幂，但基本思想是相同的。

Imagine a group of thirsty people sitting in a single row of a stadium on a hot day. Suppose we have a vendor on the aisle who can hand the first person in the row a cup, and that person will either drink it if she is thirsty or pass it on to the next person, who will follow the same behavior. Here, the constraints are the ability of the vendor to hand out new cups and the size of each cup. If very few people are in the row, the water will easily satisfy everyone’s thirst. However, as we add more people to the row, if everyone drinks the same amount as she did before, the water will never reach the people located at the end of the row. But if everyone’s thirst is reduced—that is, if we metaphorically lower each person’s metabolism—then everyone’s thirst can be satisfied. To sustain longer rows we need patrons who are less thirsty. We can even quantify how much less thirsty they must be: in the case of our stadium it is 1 over the number of patrons (giving us a power of −1 for thirst per person, and of 0 for total thirst). Thus, when we add an eighth person, if everyone’s thirst goes down by one-eighth, the existing amount of water will still suffice. Moving from our one-dimensional stadium to three-dimensional biological systems is more involved and leads to a power of −¼ for metabolism per unit of mass and a power of ¾ for total metabolism, but the fundamental idea is the same.

因此，我们现在有了一个简单的生物学关系，以幂律的形式出现。它为我们周围的世界提供了一个巧妙的总结，以及这种定律存在的可识别原因：物理约束。当然，这里的“定律”概念更像是道路上的限速标志（这只是一个好主意），而不是重力等固定定律，因为我们确实看到了一些违规行为。例如，灵长类动物和鹦鹉的寿命大约是使用缩放定律预测的两倍。这可能与它们相对较大的大脑实现进化潜力所需的较长发育阶段有关。人类甚至是一个更大的异类，可能是因为卫生条件和医疗条件的改善（从而使我们的寿命远远超过预期的四十年）。一些家养动物，如狗和猫，甚至可能是牛和马，也表现出色。这可能是由于驯化和人工选择。因此，考虑到缩放定律，小狗的寿命往往比大狗长，这有点奇怪（不过，购买宠物的父母要小心，老鼠、豚鼠和兔子的寿命往往比大狗长）。会飞的动物，包括鸟类和蝙蝠，往往比预期的寿命长。如果飞行意味着新陈代谢较低，这可能并不太令人惊讶，但事实恰恰相反，因为拍打翅膀需要更多的心跳，而不是更少。

So we now have a simple biological relationship, in the form of a power law. It provides a nifty summary of the world around us, along with an identifiable reason for why such a law exists: physical constraints. Of course, the notion of “law” here is more along the lines of posted speed limits on a road (it is just a good idea) versus a fixed law such as gravity, as we do see some violations. For example, primates and parrots live about twice as long as one would predict using the scaling law. This may be tied to the longer developmental stages needed for their relatively bigger brains to realize their evolutionary potential. Humans are even greater outliers, likely because of improved sanitation and medicine (thus allowing us to live far longer than the expected forty years). Some domestic animals, such as dogs and cats and perhaps even cattle and horses, also overperform. This may be due to domestication and artificial selection. Thus—and oddly, given the scaling law—small dogs tend to live longer than large ones (though mice, guinea pigs, and rabbits tend to line up as expected, pet-buying parents beware). Animals that fly, including both birds and bats, tend to live longer than expected. This might not be too surprising if flying somehow implied lower metabolism, but the opposite is true, as beating wings require more heartbeats, not fewer.

虽然如果“定律”完美地发挥作用会很好，但即使不完美的定律也是有用的。在科学中，我们经常面临在对某些具体事物有完全理解和对许多事物有不完全理解之间需要权衡。例如，在生物学中，人们花费了大量精力试图了解单个生物体，而且有些生物学家专门研究某种蠕虫（以及该物种中的特定方面）。虽然这些研究提供了关键的见解，但 Murray Gell-Mann 的“粗略地看待整体”表明，即使这些努力有时会失败，能够在广泛领域发展普遍的见解也是有力量的。事实上，这种失败往往会带来新的见解。因此，如果我们小心不要讲出这样的故事，那么了解大脑或驯养的生物往往不遵循一般的缩放定律可能会给我们带来一些新的见解。

While it would be nice if the “law” worked perfectly, even an imperfect law is useful. In science we often face trade-offs between having a complete understanding of some specific thing and an incomplete understanding of many things. In biology, for example, a huge amount of effort has been spent trying to understand single organisms, and there are biologists who specialize in a particular species of worm (and, within that species, specific aspects therein). While such studies provide key insights, Murray Gell-Mann’s “crude look at the whole” suggests that there is power in being able to develop generalized insights across broad domains, even if these efforts sometimes fail. Indeed, such failures often provide new insights. Thus, knowing that big-brained or domesticated creatures tend not to follow the general scaling law may give us some new insights if we are careful not to tell just-so stories.

在一个领域找到普遍规律可能会启发我们寻找其他领域的相关规律。如果生物系统面临导致缩放规律的约束，那么其他系统可能也会如此。

Finding a general law in one area may inspire us to search for related laws in other domains. If biological systems face constraints leading to scaling laws, then perhaps other systems do so as well.

刘易斯·弗莱·理查森率先采用了现代技术来预测天气和战争。在他的《致命争吵统计》（1950 年）中，他为战争赋予了统计的面貌。表 9.1 显示了他的一些关键数据。可以看出，一场战争中死亡人数越多，我们观察到的战争就越少（谢天谢地）。括号中的数字为数据提供了一些有用的近似值，利用这些近似值，我们可以看到，随着死亡人数增加十倍，战争数量减少了三倍。

Lewis Fry Richardson pioneered modern techniques for forecasting both the weather and wars. In his Statistics of Deadly Quarrels (1950) he gave war a statistical face. Table 9.1 shows some of his key data. As can be seen, the higher the number of deaths in a given war, the fewer such wars we observe (thankfully). The numbers in parentheses provide some useful approximations to the data, and using these, we can see that as deaths increase by a factor of ten, the number of wars decreases by a factor of three.

理查森的发现可以转化为幂律语言。这样做，我们发现战争数量与死亡人数的 −½ 次方成正比。这意味着，当你将死亡人数翻倍时，预期的战争数量是之前值的 70%。这种关系的一个含义是，我们应该预计在某个时候会有一场造成约 4200 万人死亡的战争。当然，幂律并没有告诉我们这样的战争何时会发生，只是告诉我们，如果预测分布成立，就会有一场这样的战争。

Richardson’s findings can be translated into the language of power laws. Doing so, we find that the number of wars is proportionate to the number of deaths raised to roughly the −½ power. This implies that when you double the number of deaths, the expected number of wars is 70 percent of the previous value. One implication of this relationship is that we should expect one war with around 42 million deaths at some point. Of course, the power law doesn’t tell us when such a war will happen, only that one such war is expected if the predicted distribution holds.

战争死亡人数

Approximate Deaths Number of Wars

10,000,000 (10 7 ) 2 (2 × 3 0 )

10,000,000 (107) 2 (2 × 30)

1,000,000 (10 6 ) 5 (2 × 3 1 )

1,000,000 (106) 5 (2 × 31)

100,000 (10 5 ) 24 (2 × 3 2 )

100,000 (105) 24 (2 × 32)

10,000（104 ） 63（2× 33）

10,000 (104) 63 (2 × 33)

1,000（103 ） 188（2× 34）

1,000 (103) 188 (2 × 34)

表 9.1： 1820 年至 1945 年战争死亡人数，摘自 Richardson (1950)。括号中的数值为数据提供了有用的近似值。

Table 9.1: Deaths in warfare, 1820–1945, from Richardson (1950). The values in parentheses provide useful approximations to the data.

乔治·金斯利·齐普夫 (George Kingsley Zipf) 是一位美国语言学家，他对语言中词汇使用的统计数据很感兴趣。如果我们计算文本中各种单词出现的次数，就会发现有些单词的使用频率远远高于其他单词，这并不奇怪。单词的使用频率（由其等级指定）由幂律描述，指数为 −1。因此，文本中第二常用的单词出现的频率大约是使用频率最高的单词的一半。第三常见单词出现的频率是三分之一，依此类推。这种关系适用于多种语言（包括随机生成的语言）。

George Kingsley Zipf was an American linguist interested in the statistics underlying word use in languages. It’s not too surprising that if we count the number of occurrences of various words in a text, we find that some words are used far more often than others. The frequency with which a word is used (designated by its rank) is described by a power law with an exponent of −1. So the word that is the second most commonly used in a text will occur about half as often as the word that’s most commonly used. The third-most-common word occurs one-third as often, and so on. This relationship holds across a variety of languages (including languages that are randomly generated).

类似 Zipf 的定律也适用于其他情况。例如，城市或公司规模的分布也遵循 Zipf 定律。一个国家中最大的城市人口大约是第二大城市的两倍，是第三大城市的三倍，等等。与 Zipf 的语言定律一样，这种关系适用于各种不同的情况（例如不同的国家或时间段），因此，与以前一样，这些观察结果似乎具有一定的普遍性。

Zipf-like laws occur in other contexts as well. For example, the distribution of the size of cities or corporations also follows Zipf’s law. The largest city in a country has about twice the population of the second-largest, three times that of the third-largest, and so on. As with Zipf’s law of languages, this relationship holds across a variety of different contexts (such as different countries or time periods), so, as before, there appears to be a certain universality in these observations.

尺度定律或许能为我们人类的生存能力提供一些有用的见解。世界人口约为 70 亿，每年以 1% 左右的速度增长（这意味着每 70 年人口数量就会翻一番）。纵观人类历史，大多数人生活在农村地区，但居住在城市的人口比例一直在稳步增加。就在最近，这种平衡发生了足够大的变化，如今世界上大多数人口都居住在城市。

Scaling laws may provide some useful insights into our ability to survive as a species. World population is roughly 7 billion people, and it is growing at about 1 percent per year (which implies that it will double in size every seventy years). Throughout human history, the majority of people lived in rural areas, though the proportion of people living in urban areas has been steadily increasing. Just recently the balance has shifted enough so that the majority of the world’s population now lives in cities.

城市与生物体并没有太大区别。它们的新陈代谢与各种交通和通信网络中的能量和人员流动有关，这些网络产生知识和经济产出，同时产生各种废物流，这些废物流被处理并排放到周围的空气、水和土地中。因此，认为类似的普遍性可能并不太牵强我们在生物系统中看到的现象可能也适用于人造系统，如果是这样的话，城市系统可能受相关尺度定律的支配。如果存在这样的定律，它们可能会让我们对人类的未来有所了解。

Cities are not all that different from biological organisms. They have metabolisms tied to the flow of energy and people along various transportation and communication networks that produce knowledge and economic outputs along with various streams of waste that get processed and released into the surrounding air, water, and land. So it may not be too far-fetched to think that universalities similar to what we see in biological systems might also apply to human-made ones, and if that is the case, urban systems may be governed by related scaling laws. If such laws exist, they may give us some insights into what the future holds for humankind.

Luis Bettencourt、José Lobo、Deborah Strumsky、Geoffrey West 及其同事计算了与城市人口规模相关的各种城市指标的幂律系数。一些指标（例如道路表面或汽油销售量）呈亚线性增长，这意味着随着城市人口的增加，每个人使用的资源会减少。也就是说，大城市的汽油销售量和人均道路表面面积往往低于小城市。直观上看，这是有道理的，因为城市倾向于向上而不是向外发展，这需要更少的道路，使公共交通更加可行，并导致整体上更节能的交通——一般来说，大城市往往会节省此类基础设施。还有其他指标，例如经济产出、发明活动（以专利或研发就业量衡量）、犯罪和疾病，呈超线性增长。因此，大城市比小城市在经济上更具生产力和创造力，同时也更易发生犯罪和疾病。这种超线性往往与城市的社会因素有关。最后，许多指标（主要与个人需求相关，如住房、家庭资源消费和就业）呈线性增长，这意味着按人均计算，所有城市都是一样的。

Luis Bettencourt, José Lobo, Deborah Strumsky, Geoffrey West, and colleagues have calculated power law coefficients for a variety of urban metrics tied to a city’s population size. Some metrics, such as the amount of road surface or gasoline sales, scale sublinearly, implying that as the population of a city gets larger, each person uses less of that resource. That is, bigger cities tend to have lower gasoline sales and less road surface per capita than smaller ones. Intuitively, this makes sense, as cities tend to build up rather than out, and that requires fewer roads, makes public transportation more viable, and leads to more energy-­efficient transportation overall—in general, larger cities tend to economize on such infrastructure. There are other metrics, such as economic output, inventive activity (measured by, say, patents or R&D employment), crime, and disease, that scale superlinearly. Thus, larger cities are relatively more economically productive and creative than smaller cities, along with being more crime- and disease-ridden. This superlinearity tends to be tied to the more social elements of cities. Finally, a number of metrics, mostly linked to individual human needs such as housing, consumption of household resources, and employment, scale linearly, implying that on a per capita basis, all cities are the same.

这些幂律系数是基于现有数据的初步估计。此外，它们仅提供了情况的快照，随着我们迁入与现在规模大不相同的城市，或者随着新发明改变我们的机会，我们可能会看到这些定律出现分歧，因为增长限制开始生效，或者新的技术救生筏开始部署。尽管如此，它们确实让我们看到了未来的趋势。

These power law coefficients are preliminary estimates based on existing data. Moreover, they provide only a snapshot of the situation, and as we move to cities of vastly different size from those we have now, or as new inventions alter our opportunities, we might see these laws diverge as limits to growth start to bind or as new technological life rafts are deployed. Nonetheless, they do provide a sense of our future.

如果这些估计属实，那么随着世界人口的增长，越来越多的人将聚集在城市地区，特大城市将减轻对道路和燃料等资源的需求。不幸的是，城市化进程的加快并不能缓解住房和电力等个人需求的线性增长。

If the estimates are to be believed, as the world’s population grows, concentrating more and more people in urban areas, megacities will relieve some of the demands for resources such as roads and fuel. Unfortunately, increasing urbanization will not mitigate the demands for individual needs, such as housing and electricity, which rise linearly.

超线性因素很可能掌握着我们未来的关键。犯罪和疾病等旧有的祸患——大多数科幻电影的反乌托邦观点中都突出了这些祸患——可能会随着城市规模的扩大而人均增加。与这种不幸的祸患规模扩大相平衡的是新兴大城市人均经济增长和创造力增长的前景。

It’s the superlinear factors that likely hold the key to our future. The old woes of crime and disease—prominently ­featured in the dystopian views of most science fiction ­movies—will likely increase per capita as cities become bigger. Balancing this unfortunate scaling of woes is the prospect of per capita increases in economic growth and inventiveness in the emerging megacities.

就像心脏稳定的跳动一样，世界人口不断增长并向城市中心集中。也许正是在这样的集中中，才会迸发出创造性的火花，让我们能够延长生命，超越规定的跳动次数。

Like the steady beat of a heart, world population continues to grow and concentrate into urban centers. Perhaps out of such concentrations, an inventive spark will emerge that allows us to prolong our existence beyond the allotted number of beats.

十

ten

从水神殿到进化的机器：合作

From Water Temples to Evolving Machines: Cooperation

现在，你们的手牵着手，心连着心。

Now join your hands, and with your hands your hearts.

—威廉·莎士比亚，《亨利六世》

—William Shakespeare, Henry VI

乙过去几个世纪以来，阿利尼西亚农民一直在梯田山坡上种植水稻（见图 10.1）。水稻需要水，因为控制稻田生态系统生产的几个重要的生化循环，如土壤 pH 值、温度、养分循环、有氧条件和微生物生长，都与精心控制的水流直接相关。因此，伴随梯田的是一套复杂的重力灌溉系统，该系统依赖于季节性河流、地下水流以及各种灌溉渠道、隧道和引水堰的建造和维护。虽然这些灌溉工程令人印象深刻——特别是考虑到使用手工工具和原始的测量仪器挖掘千米长的隧道等的难度——但它们无法克服固有的水资源稀缺性。

Balinese farmers have grown rice on terraced hillsides for the last few centuries (see Figure 10.1). Rice demands water, as several important biochemical cycles that govern the production of the rice paddy ecosystem, such as soil pH, temperature, nutrient circulation, aerobic conditions, and microorganism growth, are directly tied to the carefully controlled flow of water. Thus, accompanying the terraces is an elaborate, gravity-fed irrigation system dependent on seasonal rivers, groundwater flows, and the creation and maintenance of various irrigation canals, tunnels, and diversion weirs. While these irrigation works are impressive—especially considering the difficulty of digging kilometer-long tunnels and the like using hand tools and primitive surveying instruments—they cannot overcome the inherent scarcity of water.

图 10.1：巴厘岛苏巴克帕库杜伊的水稻梯田，目前被洪水淹没以控制害虫。这些梯田是对景观的惊人改变，既代表了连贯的综合，也代表了对自然倾向的彻底改变。（照片由 J. Stephen Lansing 提供。）

Figure 10.1: Rice terraces in Subak Pakudui, Bali, currently flooded to control pests. These terraces are a striking modification of the landscape, representing both a coherent synthesis and an abject alteration of nature’s inclinations. (Photograph courtesy of J. Stephen Lansing.)

鉴于水资源稀缺，以及巴厘岛农民缺乏中央控制，经济学家预计会看到一个严酷的竞争结果，托马斯·霍布斯在《利维坦》中对此进行了最精彩的描述：“而人类的生活，孤独、贫穷、肮脏、野蛮和短暂。”这一预测是由于系统内存在外部因素——对直接交易之外的各方施加的成本或收益。在一个重力供水稀缺的世界里，我们可能预计上游农民不会理会下游农民的需求。因此，上游农民只考虑自己的利益，愿意消耗更多的水，只要这至少能使自己的产量增加一点点，即使将水流到下游可能会让其他农民获得更大的收益。在这种情况下，我们可以重新分配水，使总产量最大化——理论上，我们可以给每个农民提供和以前一样多的作物，而且还会剩下一些，这至少可以让一个人过得更好。

Given the scarce water and the lack of central control of Bali’s farmers, economists would expect to see a harsh, competitive outcome, best characterized by Thomas Hobbes in Leviathan: “And the life of man, solitary, poore, nasty, brutish, and short.” This prediction is due to the presence of externalities—costs or benefits imposed on parties outside of (external to) the immediate transaction—within the system. In a world with scarce, gravity-fed water supplies, we might expect that upstream farmers would pay no heed to the needs of downstream farmers. Thus, an upstream farmer, thinking only of her own good, is willing to consume additional water as long as it results in at least a trivial gain in her own output, even when passing that water downstream might allow other farmers to reap a much larger gain. In such a situation, we could reallocate the water and maximize the total crop—in theory we could give every farmer as much crop as she was getting before and still have some left over, which could make at least one person better off.

外部性只是个人激励导致不良结果的一个例子。竞争让你略微受益，而合作让你受益显著，这种情况太常见了。

Externalities represent just one example of where individual incentives result in inferior outcomes. Such situations, where being competitive makes you slightly better off while being cooperative makes you remarkably better off, are all too common.

尽管霍布斯对巴厘岛水稻种植的预测与事实不符，但多亏史蒂夫·兰辛及其同事的努力，我们在岛上发现了农民全系统合作的典范，从而实现了数个世纪的可持续农业。上游农民没有独占水源，而是与下游农民精心协调合作，从而实现了总体产量的大幅提升。

Notwithstanding the Hobbesian prediction for Balinese rice farming, thanks to the work of Steve Lansing and his collaborators, we find on the island an example of system-­wide cooperation among the farmers leading to many centuries of sustainable agriculture. Rather than hogging the water, the upstream farmers carefully coordinate and cooperate with the downstream ones, resulting in much larger overall harvests.

一个可能揭示这一合作之谜的线索是，我们在巴厘岛发现了一个复杂的水神庙宗教系统，它与梯田和灌溉工程的物理系统非常相似。该系统中的单个堰与神殿相关联，而这些神殿被聚合成供奉农业神的寺庙。因此，当地的堰嵌入当地寺庙，而当地寺庙又嵌入其他寺庙，这些部分的各种聚合与底层灌溉系统和物理流域密切相关。神社和寺庙的会众每年开会一次，协调每个农民的用水。

One potential clue to this cooperative mystery is that we find an elaborate religious system of water temples in Bali that closely parallels the physical system of terraces and irrigation works. Individual weirs in the system are associated with shrines, and those shrines get aggregated into temples dedicated to agricultural deities. Thus, local weirs are nested into local temples that get further nested into still other temples, with the various aggregations of these pieces being closely associated with the underlying irrigation system and the physical watershed. The congregations of the shrines and temples meet once a year to coordinate each individual farmer’s use of water.

虽然我们很想就此结束故事，但我们知道，宗教机构的出现是为了解决外部性问题，并带来了整个系统的和谐与幸福，但这样的结论远不如真正推动这个系统合作的因素有趣。

While it’s tempting to end our story here, knowing that a religious institution has arisen to solve the externality problem and has resulted in harmony and happiness throughout the system, such a conclusion is far less interesting than what really drives this system’s cooperation.

与所有农业系统一样，水稻生态系统必须克服害虫的侵袭，包括昆虫、啮齿动物、微生物及其携带的疾病。害虫有时几乎可以毁掉整个作物。害虫最终造成的损失与自然和人为因素有关，例如水流模式和收获方式​​。

Like all agricultural systems, the rice ecosystem must overcome attacks by pests, including insects, rodents, microorganisms, and the diseases they bear. Pests can sometimes destroy almost the entire crop. The ultimate amount of pest damage is tied to both natural and human factors, such as patterns of water flow and harvesting.

随着农作物的生长，害虫也随之生长。当农作物收割后，营养物质被带走，害虫种群数量急剧下降。但是，如果新休耕的田地靠近未收割的田地，害虫就会迁移过来并继续生长。后一种生态系统动态导致了巴厘岛系统中发现的第二个主要外部性——收割稻米的农民可能会给邻近的农民带来无补偿的成本，因为其作物上的害虫会迁移到邻近的作物上。

As crops grow, so do the pests. When a crop is harvested, the nutrients are removed, and pest populations crash. However, if the newly fallow field is near an unharvested field, the pests will move over and continue to grow. This latter piece of ecosystem dynamics results in the second major externality found in the Balinese system—a farmer harvesting her rice crop may impose an uncompensated cost on neighboring farmers as the pests from her crop migrate to the neighboring crops.

20 世纪 70 年代，印尼政府无意中测试了巴厘岛稻田的生态系统动态。在亚洲开发银行顾问的建议下，印度尼西亚政府对农业政策进行了大规模调整，并通过法律规定对新开发的高产品种进行双季和三季种植。这些规定导致放弃了寺庙系统（官方报告中称之为巴厘岛的“稻米崇拜”）的协调合作农业。

In the 1970s, the Indonesian government inadvertently tested the ecosystem dynamics of Bali’s rice fields. Based on advice from consultants at the Asian Development Bank, the Indonesian government undertook a massive redirection of agricultural policy and legally mandated the double- and triple-season cropping of newly developed, high-yielding varieties of rice. These mandates led to the abandonment of the temple system (noted in official reports as a Balinese “rice cult”) of coordinated, cooperative agriculture.

这一变化发生后不久，有关“供水调度混乱”和“害虫种群激增”的报告开始陆续传到地区农业办公室。害虫问题首先通过引进对现有害虫具有抗性的作物新品种得到缓解。但不幸的是，大自然找到了解决办法，这些新品种很快就被新的害虫所击败。政府报告开始读起来像一出悲剧：通过引进抗稻飞虱的水稻品种 IR-36，褐飞虱的灾害有所减少，但这种新品种的水稻很快被通格罗病毒所淹没，而引进的 PB-50 又能抵抗这种病毒，不幸的是，PB-50 容易受到稻飞虱病原体引起的褐斑病的感染，等等。在此期间，害虫造成的作物损失接近 100%，巴厘岛农民将这一时期称为poso（饥饿和歉收）时期。

Soon after this change, reports of “chaos in the water scheduling” and “explosions of pest populations” began to trickle into district agricultural offices. The pest problems that arose were first mitigated by the introduction of new crop varieties resistant to the pests at hand. Alas, nature finds a way, and these new varieties soon succumbed to new pests. Government reports begin to read like a tragic farce: the plague of brown planthoppers was reduced by the introduction of the planthopper-resistant rice strain IR-36, but this new variety of rice was quickly overwhelmed by tungro virus, which was countered by the introduction of ­PB-50, which unfortunately was susceptible to brown leaf spots caused by the H. oryzae pathogen, and so on. Crop losses due to pests approached 100 percent during this time, and Balinese farmers remember this period as a time of poso (hunger and harvest failures).

上述讨论包含了拼凑巴厘岛稻米种植合作出现所需的线索。随着灌溉系统的发展，上游农民可能忽视了下游农民的需求，随意取水。水稻需要定期洪水，因此下游农民可能只能通过抵消种植量来生存，这样他们的用水高峰发生在上游农民用水需求下降的时候。这导致了交错收获，上游农民在下游农民的作物仍在生长时收获她的作物，反之亦然。只要害虫种群适中且田地相距较远，这是一个可行的系统。然而，随着人口的增长，对水稻的需求增加，更多的梯田被开发并投入生产。这导致了更紧密的田地和单一栽培生态系统，如果农民不协调休耕期，这两个因素有利于害虫的生长及其在田地中的传播。

The discussion above contains the needed clues for piecing together the emergence of cooperation in Balinese rice farming. As the irrigation systems developed, the upstream farmers likely ignored the needs of the downstream ones and took whatever water they wanted. Rice requires periodic floods, so presumably the downstream farmers were able to exist only by offsetting their planting so that their peak use of water occurred during ebbs in the water demands of the upstream farmers. This resulted in staggered harvests, where the upstream farmer would harvest her crop while the downstream farmer’s crop was still growing and vice versa. As long as the pest populations were modest and the fields far apart, this was a workable system. As the population grew, however, the demand for rice increased and more terraces were developed and put under production. This resulted in more closely packed fields and a monocultural ecosystem, two factors that favor the growth of pests and their transmission across fields if farmers do not coordinate fallow periods.

由于上游农民可以优先获得水源，因此他们最好随心所欲地取水，并通过与下游农民休耕相同的时间将害虫造成的损害降到最低。但是，如果田间害虫流动的外部成本相对于缺水造成的损害较低，下游农民宁愿等待更大的水流量，也不愿休耕相同的时间。在这种情况下，农民会发现自己处于一种类似于棒球投手和击球手之间的决斗的战略境地，投手希望将球投向击球手没有挥棒的地方。

Since the upstream farmers have first access to the water, they are best off if they take as much water as they want and minimize damage from pests by having the same fallow periods as the downstream farmers. However, if the externality costs of the pests flowing between the fields are low relative to the damage caused by scarce water, the downstream farmers would rather wait for the bigger water flows and not have identical fallow periods. Under such conditions, the farmers find themselves in a strategic situation akin to a duel between a baseball pitcher and a batter, where the pitcher wants to throw the ball where the batter isn’t swinging.

然而，随着害虫造成的损失不断增加，系统范围内的显著转变成为可能。如果如果害虫造成的外部成本超过水资源匮乏造成的成本，下游农民就会希望与上游农民合作并同时种植，因为现在因水资源匮乏而损失总比因虫害而损失要好。当这种情况发生时，就会出现一种新的平衡，农民们进行协调，使两块田地同时休耕，杀死害虫。在某些条件下，增加虫害造成的损失可以增加农作物的总产量，这有点违反直觉。之所以发生这种情况，是因为随着虫害变得越来越严重，它们会导致系统转变为一种合作机制，在这种机制下，农民们协调种植，并且由于两个农民都支付了虫害成本（现在可以避免），而只有下游农民支付水资源匮乏的成本，因此系统的总产量就会增加。

As the damage from pests increases, however, a remarkable system-wide transition becomes possible. If the external costs from pests exceed those from scarce water, downstream farmers will want to cooperate and plant at the same time as the upstream farmers, since now it is better to lose due to water scarcity than to pest damage. When this happens, a new equilibrium becomes possible in which the farmers coordinate so that both fields simultaneously lie fallow, killing off the pests. Under certain conditions, increasing the amount of damage caused by pests can, rather counterintuitively, increase the total output of crops. This occurs because as pests become worse, they cause the system to transition into a cooperative regime under which the farmers coordinate planting, and since both farmers pay a cost (now avoided) from pests while only the downstream farmer pays a cost from water scarcity, the total production in the system increases.

那么，如果合作的动机与农民的成本和收益如此直接相关，我们为什么会看到寺庙呢？要合作，农民需要协调。因此，某种机构——水神庙——可以充当协调工具。由于所有农民都希望协调，因此寻求和遵循寺庙给出的任何建议符合他们的自身利益。即使没有武力威胁、对灾难的恐惧或排斥，水神庙也有一种隐含的权力来决定所有农民的种植时间（见图 10.2）。

So why do we see temples if the motivation for cooperation is so directly tied to the farmers’ costs and benefits? To cooperate, the farmers need to coordinate. Thus, there is a role for some type of institution—the water temples—to serve as a coordination device. Since all farmers want to coordinate, it is in their self-interest to seek and follow whatever advice is given by the temples. Even without threats of force, fear of calamity, or ostracism, the water temples have an implicit power to dictate planting times to all of the farmers (see Figure 10.2).

图 10.2： 2011 年 3 月，巴厘岛，在十月伊卡卡月满月节期间，人们向湖神献祭。这座寺庙控制着各种灌溉系统通往生态系统中一个关键水库的通道。（照片由 J. Stephen Lansing 友情提供。）

Figure 10.2: Offerings to the Goddess of the Lake during the festival of the full moon of the tenth Icaka month on the island of Bali, March 2011. This temple controls the access of various irrigation systems to a key water reservoir in the ecosystem. (Photograph courtesy of J. Stephen Lansing.)

巴厘岛的农业故事是一个复杂系统中合作的故事。我们首先从表面上看应该是灾难性的情况开始，上游的农民只关注自己的福利，独占了所有的水资源，导致农作物产量大幅下降。然后我们添加了一组复杂的动态因素，包括自然和人为因素，这些因素重新调整了激励机制，使合作成为可能，农作物产量增加，使每个人都过得更好。为了实现这一新结果，需要一种协调机制，因此为宗教机构开辟了一个新的社会空间，它不是实践某种任意的意识形态，而是受潜在的水文、作物生长模式和害虫种群动态的驱动，无论它的创始人或实践者是否真正意识到这一点。复杂的自然和社会系统的相互作用使整个系统比没有这种系统时要好得多。

The story of farming in Bali is a tale of cooperation arising in a complex system. We began with what, on the face of it, should be a disastrous situation in which upstream farmers, paying attention to only their own welfare, hog all the water, resulting in a greatly diminished output of crops. Then we added a complex set of dynamics, both natural and human, that realigned incentives in such a way that cooperation became possible and crop output increased, making everyone better off. To realize this new outcome, there was a need for a coordination device, and thus a new social niche opened up for a religious institution that, rather than practicing some arbitrary ideology, was in fact driven by the underlying hydrology, crop growth patterns, and pest population dynamics, regardless of whether any of its founders or practitioners actually realize it. The interaction of complex natural and social systems led the entire system to a remarkably better place than would otherwise arise.

在生存斗争中，合作是一种往往能提供决定性优势的策略。正如丁尼生所说，“尽管大自然可能“凶残无比”，但合作而非竞争的能力往往能让一个群体获得远远超出其明显能力的繁荣。合作可以发挥适应性的作用，这方面的例子在各个层面都比比皆是。细菌对宿主的伤害很小，但一群细菌通过一组化学信号协调攻击，却能致命。小鱼很容易成为捕食者的目标，而一群这样的鱼却可以相对不受惩罚地移动。人类群体，无论是在村庄里进行贸易，还是在军队中作战，都比他们孤独的同胞更有可能生存下来。

In the struggle for survival, cooperation is one strategy that tends to provide a definitive edge. “Tho’ Nature,” as Tennyson says, may be “red in tooth and claw,” the ability to cooperate rather than compete often allows a group to thrive far beyond its apparent means. Cooperation leverages fitness, and examples of this abound across all levels of existence. A bacterium can do little harm to a host, yet a group of bacteria, coordinating their attack through a set of chemical signals, is deadly. A small fish is an easy target for a predator, while a school of such fish can move with relative impunity. Humans in groups, whether undertaking trade in a village or fighting within an army, are far more likely to survive than their solitary brethren.

因此，理解合作如何产生并维持是进一步理解相互作用的主体如何在复杂世界中生存的关键问题。巴厘岛水稻种植的案例说明了一种方法。为了理解该系统的内在复杂性，需要来自各个科学领域的各种贡献。人类学家研究了岛上当前的农业和宗教习俗，并与考古学家一起重建了过去的习俗。历史学家调查了绿色革命对巴厘岛农业的影响政策。生物学家、农业专家、水文学家和地理学家对生态系统有了深刻的了解，描述了农作物、水和害虫之间的所有相互作用。计算机科学家开发了基于代理的模型，让农民对作物选择做出适应性决策。我和一位人类学家利用博弈论的思想开发了上面使用的上游和下游农民之间选择的稀疏模型。我们一起把拼图的各个部分拼凑在一起，并编写了一个连贯的故事，讲述了巴厘岛合作的出现和维持。

Thus, understanding how cooperation can emerge and be maintained is a key issue in furthering our understanding of how interacting agents survive in complex worlds. The case of Balinese rice farming illustrates one approach. To understand the embedded complexities of that system, it took a variety of contributions from across the sciences. Anthropologists looked at current farming and religious practices on the island and, in conjunction with archaeologists, reconstructed past practices. Historians investigated the impact of the green revolution on Balinese agricultural policy. Biologists, agricultural specialists, hydrologists, and geographers developed insights about the ecosystem, delineating all of the interactions among crops, water, and pests. Computer scientists developed agent-based models of farmers making adaptive decisions about cropping choices. An anthropologist and I used ideas from game theory to develop the sparse model of choice between upstream and downstream farmers used above. Together, we were able to put together the various pieces of the puzzle and develop a coherent story of the emergence and maintenance of cooperation on Bali.

当然，这些见解需要大量的专业知识和努力。理解合作的另一种方法是依靠一个相对简单的抽象模型。这种方法可能与我和同事在巴厘岛所采取的方法截然相反。但如果我们技术娴熟，运气好，我们忽略的细节就没那么重要了，我们可以利用这个抽象模型获得一些新的普遍见解。

Of course, these insights required an amazing span of professional expertise and effort. An alternative approach to understanding cooperation is to rely on a relatively stark abstract model. Such an approach is perhaps the polar opposite of what my colleagues and I undertook on Bali. But if we are skilled, and lucky, the details that we ignore will not matter much, and we can use this abstract model to gain some new general insights.

探索合作的典型问题被称为囚徒困境。在最初的版本中，两名同谋者刚刚被警方逮捕，并被关押在不同的牢房中。尽管警方怀疑他们犯有死罪，但证据不足，因此如果两名囚犯都不认罪，两人都将被判入狱一年。警方向每名囚犯提出以下交易：如果他认罪并成为国家证人，那么他就可以自由出狱，但他的同谋将被处死。这笔交易的唯一条件是，如果两名囚犯都认罪，每人将被判入狱十年。每个囚犯都必须在不知道同谋者是否认罪的情况下决定怎么做。

The quintessential, stylized problem for exploring cooperation is known as the prisoner’s dilemma. In its original version, two co-conspirators have just been apprehended by the police and placed in separate cells. Although the police suspect them of committing a capital crime, there is little evidence, so if neither prisoner confesses, both will be jailed for one year. The police offer each prisoner the following deal: if he confesses and becomes a witness for the state, then he can go free, though his accomplice will be put to death. The only proviso to this deal is that if both prisoners confess, each will be jailed for ten years. Each prisoner must decide what to do without any knowledge of whether the co-conspirator has confessed.

每个囚犯都面临着一个有趣的困境。如果他坦白而他的同伙保持沉默，那么他将获得自由，而不是在监狱里呆一年。同样，如果他坦白而他的同伙也坦白，那么他将只会被判处十年监禁，而不是被处死。无论同伙做什么，囚犯坦白总是更好的选择，也就是说，背叛他的同伙。当然，两个囚犯都面临着同样的情况，所以对他们两个来说，坦白都是有利的，这意味着他们都将在监狱里呆十年。相反，如果他们能够合作并保持沉默，他们只会被判入狱一年。正如我们之前所看到的，虽然竞争会让你的情况略有好转，但合作会让你的情况好转很多。

Each prisoner faces an interesting dilemma. If he confesses and his accomplice stays quiet, then he will go free rather than spending a year in jail. Similarly, if he confesses and his accomplice also confesses, then he will only get ten years in jail instead of being put to death. Regardless of what the accomplice does, the prisoner is always better off confessing, that is, defecting on his accomplice. Of course, both prisoners face the same situation, so for both of them it is in their interest to confess, which means that they both will spend ten years in jail. If, instead, they could have cooperated and stayed quiet, they would have been jailed for only a year. As we saw before, while being competitive makes you slightly better off, being cooperative makes you remarkably better off.

如果囚徒困境只涉及囚徒，那它就没什么意思了。然而，这里的基本框架涵盖了许多有趣的场景。在战场上，敌对双方可以选择进行可预测的、被动的武力展示，这样既能保证自己的安全，又能阻止指挥官的行动（即他们可以合作），或者双方都可以攻击对方（即他们可以叛变）。正在狩猎的步兵或母狮可以留在前线（合作），也可以后退一点，让其他人首当其冲（叛变）。两家竞争对手可以心照不宣地保持高价（合作）或向客户提供隐藏折扣（叛变）。渔民可以限制捕捞量以维持鱼类的繁殖量（合作），也可以在别人不注意的时候违反这些限制（叛变）。污染者可以限制二氧化碳的排放量（合作）或不限制（叛变）。细菌可以同时释放毒素（合作），也可以避免释放毒素并节省能源（缺陷）。eBay 上的卖家可以准确描述他们的商品并完成销售（合作），也可以在销售前或销售后误导消费者（缺陷）。等等。

If the prisoner’s dilemma were only about prisoners, it would be of passing interest. However, the basic framework here captures many interesting scenarios. Opposing soldiers dug into trenches on a battlefield can choose to make a predictable and passive show of force that both allows them to stay safe and keeps their commanding officers at bay (that is, they can cooperate), or each side can attack the other (that is, they can defect). Infantryman or lionesses on the hunt can stay at the front of the line (cooperate) or fall back a bit to let others bear the brunt of the attack (defect). Two rival firms can tacitly keep their prices high (cooperate) or provide hidden discounts to customers (defect). Fishermen can limit their catches to maintain a reproductive stock of fish (cooperate) or can violate such limits when others are not looking (defect). Polluters can limit their output of carbon dioxide (cooperate) or not (defect). Bacteria can release a toxin simultaneously (cooperate) or avoid doing so and save on energy (defect). Sellers on eBay can accurately describe their items and follow through on sales (cooperate) or be misleading before or after the sale (defect). And on and on.

请注意，“合作”和“背叛”这两个标签仅捕捉了个体行为和各自的动机。它们并不反映社会的目标。在某些情况下，例如竞争公司设定高价或低价，合作导致缺乏竞争和高价是一种不好的社会结果。在其他情况下，例如渔业，让渔民合作并限制捕捞量以确保鱼类资源得到维持是一种良好的社会结果。无论如何，在没有缓解因素的情况下，囚徒困境的逻辑会导致背叛——如果我们是石油等产品的消费者，这是一个好的结果，如果我们关心地球的渔业和二氧化碳水平，这是一个糟糕的结果。

Note that the labels “cooperate” and “defect” capture only the actions and respective incentives of the individual agents. They do not reflect the goals of society. In some cases, such as the rival firms setting either high or low prices, cooperation leading to a lack of competition and high prices is a bad social outcome. In other cases, such as the fisheries, having fishermen cooperate and limit their catch in order to ensure that the stock of fish can be maintained is a good social outcome. Regardless, in the absence of mitigating factors, the logic of the prisoner’s dilemma leads to defection—which is a good outcome if we are consumers of a product such as oil and a bad one if we care about our planet’s fisheries and carbon dioxide level.

如果我们处在上文描述的囚徒困境中，那么叛逃是显而易见的结果。但是，如果我们改变一些基本条件，合作可能会成为更合理的结果。例如，两名囚犯不允许互相交流，但如果他们能够交流（并相信对方的话），他们就会同意保持沉默。游戏的另一个鼓励背叛的特点是其一次性性质。当玩家只互动一次时，“无论其他玩家做什么，我最好背叛”的逻辑成立。然而，如果玩家要反复玩游戏，那么未来的阴影就会变得重要，合作就会成为一个有吸引力的选择，因为背叛的短期收益可能会被长期合作收益的潜力所淹没。

Defection is the obvious outcome to predict if we are in the stark prisoner’s dilemma world described above. However, if we alter some of the underlying conditions, cooperation may become a more reasonable outcome. For example, the two prisoners were not allowed to communicate with each other, yet if they could communicate (and trust each other’s word), they would agree to stay quiet. Another feature of the game that encourages defection is its one-shot nature. When the players interact only a single time, the logic of “regardless of what the other player does, I’ll be better off defecting” holds. However, if the players are going to play the game repeatedly, then the shadow of the future becomes important and cooperation becomes an attractive choice, since the short-term gain of defecting can be overwhelmed by the potential for a longer stream of cooperative benefits.

人们以多种方式研究了囚徒困境中的合作。一种方法是研究现实世界中的案例，例如第一次世界大战期间的堑壕战或缅因州龙虾渔民的行为。另一种方法是使用博弈论的数学工具来探索非常抽象的世界中合作的极限。第三种方法是使用实​​验来研究博弈，无论是在实验室还是在现场，我们在随机和受控的条件下观察受试者（从大学生到培养皿中的细菌）。所有这些技术都为合作的起源提供了有用的见解。

Cooperation in the prisoner’s dilemma has been studied in a variety of ways. One method is to do case studies of real-world examples, such as trench warfare during World War I or the behavior of lobster fishermen in Maine. Another approach uses the mathematical tools of game theory to explore the limits of cooperation in a very abstract world. A third approach studies the game using experiments, either in the laboratory or in the field, where we observe subjects (ranging from college undergraduates to bacteria in a petri dish) under randomized and controlled conditions. All of these techniques have yielded useful insights into the origins of cooperation.

不同的方法各有优缺点。案例研究提供了在现实世界中合作的直接证据，尽管由于实际事件的复杂性，收集所需的历史数据并对其进行分析往往很困难。数学方法为问题提供了很好的抽象表述，但有时这种抽象可能太过鲜明。例如，一场肯定会在一千轮后结束的重复博弈与一场预计只会在一千轮后结束的重复博弈的结果截然不同——在前一种情况下，已知的最后一轮会导致该轮的背叛，最终在之前的所有轮次中瓦解，导致整个博弈过程中相互背叛，而在后一种情况下，最后一轮的不确定性使合作策略成为可能。实验在让我们了解建立和维持合作所需的条件方面非常有用，尽管我们经常受到可以使用的受试者、发现其潜在策略的能力以及创建合适实验环境的困难的限制。

The different approaches all have strengths and weaknesses. Case studies provide direct evidence of cooperation arising in real-world contexts, though it is often hard to gather the needed historical data and analyze it given the complexities involved in the actual events. Mathematical approaches provide a nice abstract formulation of the problem, but at times such abstractions can be too stark. For example, a repeated game that is certain to end after a thousand rounds results in a dramatically different outcome from one that is only expected to end after a thousand rounds—in the former case the known final round leads to a defection on that round, which eventually unravels through all of the previous rounds, leading to mutual defection throughout the game, while in the latter case the uncertainty of the final round makes cooperative strategies possible. Experiments have been extremely useful in giving us some sense of the conditions needed to establish and maintain cooperation, though we are often limited by the subjects we can use, by our ability to uncover their underlying strategies, and by difficulties in creating suitable experimental environments.

为了进一步了解合作，我们需要创造新的方法，以便更好地了解合作问题。在过去的二十年里，我和同事们一直在开发一种高科技混合技术，将以前做过的工作结合起来。它为了解复杂系统中合作的出现提供了一个重要的新窗口。

To further our understanding of cooperation, we need to create new approaches that will allow us to gain better insights into the problem of cooperation. Over the last two decades, colleagues and I have been developing a high-technology hybrid of what has been done before. It has provided an important new window into the emergence of cooperation in complex systems.

这种新方法背后的想法是在计算机内部创建一个人工世界。与案例研究一样，我们希望允许代理之间进行一组相当复杂的交互，这些交互可以主动适应它们的经验。与数学方法一样，我们希望依赖一些核心的、易处理的、抽象的概念，这些概念可以提供所需的结构和方向。与实验方法一样，我们希望能够仔细观察和操纵我们的代理在其中交互的世界。最后，这种方法结合了计算机科学、博弈论、数学和生物学的关键思想，为我们提供了合作的新视角。

The idea behind this new approach is to create an artificial world inside a computer. As with case studies, we want to allow for a fairly complex set of interactions among agents that can actively adapt to their experiences. As with the mathematical approach, we want to rely on some core, tractable, abstract concepts that can provide the needed structure and direction. As with the experimental approach, we want to be able to carefully observe and manipulate the world in which our agents interact. In the end, the approach combines key ideas from computer science, game theory, mathematics, and biology to give us a new view of cooperation.

这种新方法的各个元素都很简单。我们使用重复囚徒困境博弈作为系统的基础物理原理。我们虚拟世界中的代理通过根据前几个时期发生的事情提交一系列合作或背叛行动来相互对抗，然后获得游戏给出的回报（在这里，玩家获得的不是监禁，而是适当比例的积分）。

Each of the various elements of this new approach is simple. We use the repeated prisoner’s dilemma game as the foundational physics of the system. Agents in our artificial world play against one another by submitting a sequence of either cooperate or defect actions based on what happened in the previous periods, and then receive payoffs given by the game (here, instead of prison sentences, players receive appropriately scaled points).

每个玩家的策略都由一台称为有限自动机的简单计算机器表示。这些机器由一组内部状态组成，每个状态指示要采取的行动，并根据观察到的对手的行动，将一组状态转换为其他状态。图 10.3 说明了这样的一个自动机。虽然自动机结构简单，但它们可以产生复杂的策略，根据条件行为、历史、计数甚至随机性对对手的行动做出反应。

Each player’s strategy is represented by a simple computing machine called a finite automaton. These machines are composed of a set of internal states, with each state dictating an action to be taken and a set of transitions to other states that depend on the observed action of the opponent. Figure 10.3 illustrates one such automaton. While automata are simple in structure, they can lead to complex strategies that react to their opponent’s actions based on conditional behavior, history, counting, and even randomness.

最后，为了让代理能够调整和改进他们的战略机器，我们使用了一种简单的人工进化版本，称为遗传算法。与现实世界中的进化一样，遗传算法根据机器在游戏中的表现来选择要复制的机器，表现更好的机器更有可能被复制。每台机器的行为都记录在其自动机的计算机编码描述中，就像 DNA 一样，这种描述会通过一些细微的变化（突变）传递给后代，这些变化可能会导致玩家行为发生微妙的变化，或者创造出 Goldschmidt 所说的“充满希望的怪物”，拥有前所未见的狡猾而聪明的策略。正如达尔文提醒我们的那样，“从如此简单的开始，无数最美丽、最奇妙的形式已经进化，并且正在进化。”

Finally, to allow the agents to adapt and improve their strategic machines, we use a simple version of artificial evolution called a genetic algorithm. As with evolution in the real world, a genetic algorithm selects machines for reproduction based on how well they are performing in the game, with the better-performing machines being more likely to be reproduced. Each machine’s behavior is captured in the computer-coded description of its automaton, and like DNA, this description is passed on to the offspring with perhaps a few slight changes (mutations) that might either lead to a subtle change in the player’s behavior or perhaps create one of Goldschmidt’s “hopeful monsters” with a heretofore unseen and deviously clever strategy. As Darwin reminds us, “From so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.”

图 10.3：一个简单的两状态自动机。最左边的图显示了一个自动机，其两个状态用带标记的圆圈表示。每个圆圈内包含自动机在进入相应状态时将采取的操作（合作 (C) 或背叛 (D)）。从每个状态出现的虚线箭头指向过渡状态，该过渡状态基于在前一阶段观察到的对手的操作（合作 (c) 或背叛 (d) — 请注意此处使用小写字母）。如果此自动机始终从其顶部状态开始，则它最初将合作（由闪电表示）。如果对手也合作，机器将遵循适当的转换箭头（中间图，实线箭头）并保持在其顶部状态，因此它将再次合作。如果对手背叛（最右边图，实线箭头），自动机将转换到其底部状态并在下次背叛。控制底部状态转换的逻辑与顶部状态的逻辑类似。因此，这个自动机首先进行合作，然后模仿对手之前的动作，这是一种有用的策略，正式称为“针锋相对”。

Figure 10.3: A simple two-state automaton. The leftmost figure shows an automaton with its two states represented by the labeled circles. Contained within each circle is the action (either cooperate (C) or defect (D)) that the automaton will take when it enters that respective state. The dashed arrows emerging from each state point to the transition state based on the observed action of the opponent in the previous period (either cooperate (c) or defect (d)—note the use of lower-case letters here). If this automaton always begins in its top state, it will initially cooperate (indicated by the lightning bolt). If the opponent also cooperates, the machine will follow the appropriate transition arrow (middle figure, solid arrow) and stay in its top state, so it will cooperate again. If the opponent defects (rightmost figure, solid arrow), the automaton transitions to its bottom state and defects next time. The logic governing transitions in the bottom state is similar to that for the top state. Thus, this automaton begins by cooperating and then mimics the opponent’s previous move, a useful strategy known formally as tit-for-tat.

虽然这个计算模型的每个元素都很简单，但该模型创建的人造世界却并不简单。我们首先随机生成机器。在这样的世界中几乎没有秩序，因为每台机器都会循环各种状态，发出随机的合作和背叛序列。在这种环境中，由于策略随机赋予时赋予的随机运气，背叛次数多于正常的机器将比平均水平表现更好，因为在对手没有任何秩序的情况下，背叛会带来更高的收益。因此，该系统的初始进化有利于背叛次数更多的机器，而随着背叛接管我们的计算生态系统，在我们随机创造的生活混乱中，出现了一波血腥的秩序浪潮。

While each of the elements of this computational model is simple, the artificial world that the model creates is not. We begin by randomly generating the machines. In such a world there is little order, as each machine cycles through its various states emitting random sequences of cooperate and defect. In this environment, machines that defect more than normal, due to the stochastic luck bestowed upon them when the strategies were randomly endowed, will do better than average, because in the absence of any order on the part of the opponents, defection leads to higher payoffs. Consequently, the initial evolution of this system favors machines that defect more often, and out of the chaos of our randomly created soup of life comes a wave of order red in tooth and claw, as defection takes over our computational ecosystem.

在最初的进化浪潮中出现的机器结构出奇地好。虽然自动机可以访问大量潜在状态，但幸存的机器只使用其中的一小部分，而倾向于始终有缺陷的简单结构。尽管大型机器也可以实施始终有缺陷的策略，但这种机器在繁殖过程中对突变的敏感度远高于小型机器。鉴于大多数突变都是有害的（这导致在面对大量缺陷时进行合作），小型机器占了上风。因此，进化最初创造了一个由始终有缺陷的简单机器组成的世界。

The machines that arise during this initial wave of evolution are surprisingly well structured. While the automaton has access to a large number of potential states, the surviving machines use very few of these, favoring simple structures that always defect. Even though larger machines could also implement an always-defect strategy, such machines are far more sensitive than smaller ones to mutations during reproduction. Given that most mutations are detrimental (here leading to cooperation when facing a sea of defection), smaller machines prevail. Thus, evolution initially creates a world composed of simple machines that always defect.

想象一下在这样的世界里站稳脚跟。要想比其他玩家做得更好，唯一的办法就是以某种方式与某人建立合作关系。然而，总是合作会让你的处境更糟，因为与叛徒合作会让你的收益最低（在我们囚犯的例子中是死刑），而你的对手的收益最高（获释）。因此，如果自发出现一种总是合作的策略，那么它将成为叛徒的攻击目标，并会很快消亡。

Imagine trying to gain a foothold in such a world. The only way to do better than the other players is to somehow establish cooperation with someone. However, always cooperating would make you much worse off, as cooperating against a defector gives you the lowest payoff possible (the death penalty in the example of our prisoners) and your opponent the highest (going free). So if a strategy spontaneously arises that always cooperates, it will be an easy mark for the defectors and will quickly die out.

然而，假设两种这样的合作策略同时出现。在这种情况下，当他们相遇时，他们获得的回报远高于平均水平。不幸的是，即使是这种合作奖励也不足以抵消这些合作机器在面对大量背叛者时所遭受的损失。即使出现了少数无条件合作者，他们最终也会被背叛者淹没。因此，这也不是这个世界上合作的可行方式。

Suppose, however, that two such cooperative strategies arise simultaneously. In this case, when they meet, they achieve a payoff much higher than average. Unfortunately, even this cooperative bounty will be insufficient to offset the losses incurred when these cooperative machines play the much larger number of defectors. Even if small numbers of unconditional cooperators arise, they will eventually be overwhelmed by defectors. This, then, is also not a viable way for cooperation to arise in this world.

还有一条略有不同的路径可以实现合作。假设代理只能与少数其他代理进行交互。如果合作者能够团结一致，只在他们自己之间玩游戏，同时避免与叛逃者玩，那么他们将获得相对于世界其他地方的非常高的回报。不幸的是，我们的模型没有提供直接识别对手的明确方法，因为没有外部可观察的特征可以让机器对下一个对手做出推断或分类。即使这是可能的，机器也没有过去对手的记忆。因此，只与合作者互动是行不通的。

There is a slightly different path that could allow for the emergence of cooperation. Suppose that agents could interact with only a select few of the other agents. If, say, cooperators can stick together and only play the game among themselves while avoiding playing the defectors, then they would receive very high payoffs relative to the rest of the world. Unfortunately, our model provides no explicit way to directly recognize one’s opponents, as there are no externally observable features that would allow a machine to make some inference or categorization of its next opponent. Even if this were possible, the machines have no memory of past opponents. Thus, interacting only with cooperators is not going to work.

然而，类似于选择性互动的东西——尽管更聪明一些——确实允许在模型中出现一条开明的合作路径。虽然机器一开始无法识别对手，但随着游戏的进行，一系列动作可能会让机器相互识别。我们最初的进化浪潮导致了一个对手总是背叛的世界，因此机器可以通过最初的合作来表明它是不同的。我们看到，盲目的合作策略注定会失败，所以这种策略唯一可行的方法是，机器根据对手对合作提议的反应来改变自己的行为。如果一台机器合作，发现对手没有回应，那么机器就可以开始背叛，避免被进一步利用。相反，如果合作的举动导致对手改变行为并开始合作，那么这两台机器就可以建立相互合作，并一起做得很好。为了建立合作，需要出现一种愿意承担短期合作风险的机器（面对背叛者的世界），因为确定志同道合的机器并与之建立合作关系可能带来长期利益。它还需要避免被不愿意建立合作的对手利用——也就是说，它必须学会谨慎合作。

However, something akin to selective interaction—­albeit a bit more clever—does allow an enlightened, cooperative path to arise in the model. While machines cannot recognize their opponent at the outset, the sequence of actions that is played as the game progresses may allow machines to recognize one another. Our initial wave of evolution resulted in a world where opponents always defect, and thus a machine could signal that it is different by initially cooperating. We saw that a blind strategy of always cooperating is doomed to failure, so the only way such a strategy could work is if the machine alters its behavior based on how the opponent reacts to the cooperative overture. If a machine cooperates and finds that its opponent does not reciprocate, then the machine can start to defect and avoid being exploited further. If, instead, the cooperative moves cause the opponent to alter its behavior and begin to cooperate, then the two machines can establish mutual cooperation and do well together. To establish cooperation, a machine needs to arise that is willing to take the short-term risk of cooperating (in the face of a world of defectors), given the potential long-term benefit of identifying and establishing cooperation with a like-minded machine. It also needs to avoid being exploited by an opponent that is unwilling to establish cooperation—that is, it must learn to cautiously cooperate.

这样的机器采用了一种看似不可行的策略，即只与合作者一起玩，并（间接地）避免与背叛者一起玩。虽然机器无法明确避免与背叛者一起玩，但它们可以在游戏的初始阶段通过识别对手的类型来隐性地做到这一点。如果对手被确定为合作者，机器可以在游戏的剩余时间内建立并保持相互合作。如果对手被确定为背叛者，并且无法避免直接与他们一起玩，那么在游戏的剩余时间内相互背叛是次优解决方案。

Such a machine embraces the seemingly infeasible ideal of a strategy that plays only with cooperators and (indirectly) avoids defectors. While machines cannot explicitly avoid playing defectors, they can do so implicitly by recognizing the opponent’s type during the initial play of the game. If an opponent is identified as cooperative, the machines can establish and maintain mutual cooperation for the remainder of the game. If an opponent is identified as a defector and one cannot avoid playing them outright, mutually defecting for the remainder of the game is a second-best solution.

上述场景的一个特别有趣的方面是，这些新机器正在自发学习如何相互交流。在这里，游戏中的初始动作也充当着一种通信设备，可以发出合作或不合作的意图。因此，不断进化的机器劫持了它们的初始动作，并将其重新用作通信信号。这意味着短期内对某些对手采取不太理想的行动，以期实现建立合作的长期利益。

One particularly fascinating aspect of the above scenario is that these new machines are spontaneously learning how to communicate with one another. Here, the initial actions in a game are also serving as a communication device that either signals cooperative intent or not. Thus, the evolving machines hijack their initial actions and repurpose them to serve as communication signals. This entails a short-term cost of taking less-than-ideal actions against some opponents, in the hope of achieving the long-term benefit of establishing cooperation.

因此，即使在所有背叛者都存在的世界里，合作也会出现。如果至少两种谨慎合作的策略同时出现，它们就能获得高于平均水平的收益，而进化也会有利于它们的延续。

Thus even in a world of all defectors, cooperation can emerge. If at least two cautiously cooperative strategies emerge simultaneously, they can receive higher-than-average payoffs, and evolution will favor their perpetuation.

虽然很容易看出，少数谨慎合作的机器如何在充满叛逃者的恶劣世界中茁壮成长，并最终接管世界，但这留下了一个问题：这种策略是如何自发产生的。谨慎合作的机器体现了一种相当复杂的策略，它必须首先发出某种合作信号，然后根据对手的反应，采取适当的行动，建立合作或避免被利用。这样的策略需要一些仔细的协调。

While it is easy to see how a few cautiously cooperative machines could thrive in a nasty world of defectors and eventually take it over, that leaves the question of how such strategies can spontaneously arise in the first place. Cautiously cooperative machines embody a fairly sophisticated strategy that must first send some sort of cooperative signal, and then, based on the opponent’s response, play appropriately and either establish cooperation or avoid exploitation. Such a strategy requires some careful coordination.

这种协调可能产生的一种方式是，如果机器同时收到一组突变，这些突变会将它们重新配置为谨慎合作的策略。不幸的是，出现这样一组精心排列的突变的可能性很小——用天文学家弗雷德·霍伊尔使用的创造论类比，这就像龙卷风席卷垃圾场并组装出一架功能齐全的波音 747 飞机的可能性一样。另一种可能性是，一个突变以某种方式产生了所需的策略。虽然从表面上看，这个想法似乎同样难以置信，但实际上并非如此。如果我们从一台简单的总是有缺陷的机器开始，一个突变可能会产生两种可能的影响之一。第一种是，它将机器的单一动作从缺陷变为合作，将其变成一个总是合作的机器，从而敲响它的丧钟。另一种可能性是，一个突变会以某种方式产生所需的策略。是突变将机器转变为自动机中迄今为止未使用的部分，从而产生了一种完全不同的策略。

One way this coordination could arise is if machines simultaneously receive a set of mutations that reconfigure them into cautiously cooperative strategies. Unfortunately, the likelihood of having such a set of carefully aligned mutations is small—using the creationist-embraced analogy employed by the astronomer Fred Hoyle, it’s like the chance of a tornado sweeping through a junkyard and assembling a functional Boeing 747. The alternative is that a single mutation somehow results in the needed strategy. While on the face of it this idea seems equally implausible, in reality it is not. If we start with a simple always-defect machine, a single mutation can have one of two possible effects. The first is that it alters the single action of the machine from defect to cooperate, turning it into an always-cooperate machine and thereby sounding its death knell. The other possibility is that the mutation transitions the machine into a heretofore unused part of the automaton, resulting in a radically different strategy.

根据定义，机器的未使用部件不会受到自然界的考验。因此，这些区域发生的突变不会受到进化压力的影响，未使用的结构可以随意漂移，而不会对机器的整体性能产生任何直接影响。这种改变被称为中性突变，因为它们所做的改变不会对机器的行为产生可观察到的影响，因此不会对机器的即时适应性产生影响。因此，即使在一个简单、总是有缺陷的机器世界中，一切都不是静止的，因为这些机器的未使用部件会发生中性漂移。

By definition, unused parts of the machines are not tested against nature. Therefore, mutations that occur in these areas are not subject to evolutionary pressure, and the unused structure can drift around without any immediate impact on the machine’s overall performance. Such alterations are known as neutral mutations, since the changes they make have no observable consequences on how the machine behaves, and thus no impact on the machine’s immediate fitness. So even in a world of simple, always-defect machines, all is not static, as the unused parts of these machines undergo neutral drift.

在中性漂移中，单一突变可能会导致行为发生根本性变化，例如将始终背叛的策略转变为谨慎合作的策略。一旦我们有了几个谨慎合作的策略，进化力量就足以将系统从一个每个人都背叛的世界转变为一个充满合作的世界。因此，这里合作出现的真正问题是，两个或更多个谨慎合作策略自发出现的可能性有多大。

With neutral drift, it is possible for a single mutation to result in a radical change in behavior, such as having an always-defect strategy become a cautiously cooperative one. Once we have a couple of cautiously cooperative strategies, evolutionary forces will be sufficient to tip the system from a world where everyone defects to one filled with cooperation. So the real issue for the emergence of cooperation here is how likely is it that two or more cautiously cooperative strategies will spontaneously arise.

实现这一目标的一种方式是，所需的突变同时发生在两台机器上。这是可能的，因为进化选择和繁殖有时会导致机器的中性部分在短时间内在整个种群中复制。如果发生这种情况笔，如果中性配置正确，两台独立机器上同一位置的单一突变就可以导致两种谨慎合作的策略的产生。

One way for this to happen is that the needed mutation simultaneously occurs in two machines. This is possible, since evolutionary selection and reproduction can, at times, result in the neutral parts of a machine getting replicated across the population for short periods of time. If this happens, and if the neutral configuration is right, a single mutation at the same spot on two separate machines can lead to the creation of two cautiously cooperative strategies.

在某些情况下，即使只有一台机器谨慎合作，也足以颠覆整个系统。如果出现这样的一台机器，它的表现会比那些总是背叛的机器略差。但如果性能下降幅度不是太大，机器可能会存活下来并复制，从而在下一代中产生足够多的谨慎合作机器来颠覆整个系统。另一种可能性是，由于一台孤独的谨慎合作机器面对的对手只知道背叛，它会无意中触发一些总是背叛的机器的合作行为。总是背叛的机器从未遇到过合作行为，从进化的角度来看，它们不知道该怎么做。就像渡渡鸟第一次遇到水手一样，一台或多台屈从的总是背叛的机器可以为孤独的谨慎合作机器提供足够的适应性优势，使其能够在下一代中复制，并最终使整个系统转向合作。

There are also conditions in which even a single machine becoming cautiously cooperative is sufficient to tip the system. If a single such machine arises, it will do slightly worse than those machines that always defect. But if the degradation in performance is not too extreme, the machine may survive and replicate, resulting in enough cautiously cooperative machines in the next generation to tip the system. Another possibility is that a lone cautiously cooperative machine, since it is facing opponents that have only ever known defection, will inadvertently trigger cooperative behavior in some of the always-­defecting machines. The always-defecting machines have never encountered a cooperative action and don’t, in an evolutionary sense, know what to do. Like dodo birds meeting sailors for the first time, one or more subservient always-defect machines can provide enough of a fitness boon to the lone cautiously cooperative machine to allow it to replicate in the next generation and, eventually, tip the entire system into cooperation.

由于进化总是在寻找弱点，新的合作策略必须始终保持警惕，能够对对手的背叛做出反应，即使在全球范围内建立合作之后也是如此。否则，就有可能出现一个模仿者，它发出所有正确的握手信号来建立合作，但随后却背叛了。为了保持这种警惕，机器至少需要两种活动状态。图 10.3 所示的针锋相对足以与同类机器建立合作，但同时又避免被总是或偶尔背叛的对手严重利用。与往常一样，更先进的合作机器面临着进化压力，需要创建能够抵御可能导致机器故障的有害突变的结构。

Since evolution is always in search of weaknesses, the newly cooperative strategies must always remain vigilant and able to react to an opponent’s defection, even after cooperation has been established worldwide. If not, then there is the possibility of a mimic arising that sends all of the right handshake signals to establish cooperation but then defects. To maintain such vigilance, machines need at least two active states. Tit-for-tat, shown in Figure 10.3, is sufficient to establish cooperation with similar-type machines but, at the same time, avoids being badly exploited by an opponent that always or occasionally defects. As always, there is evolutionary pressure on the more advanced cooperative machines to create structures that can withstand deleterious mutations that might cause the machines to malfunction.

当然，促成合作的力量也可能合谋破坏合作。如果合作者很少受到背叛的考验，那么他们就会变得懒惰。如果发生这种情况，策略可能会演变成机器单纯合作的地步，无论是从游戏开始还是在确认初次握手之后。一旦发生这种情况，总是背叛（第一种情况）或模仿握手然后总是背叛（第二种情况）的机器就可以进入并接管世界。

Of course, the same forces that allow the emergence of cooperation can also conspire to destroy it. A population of cooperators can become evolutionary lazy if they are rarely tested by defection. If this happens, the strategies can drift to the point where the machines simply cooperate, either from the start of the game or after confirming the initial handshake. Once this happens, machines that always defect (in the first case) or mimic the handshake and then always defect (in the second case) can enter and take over the world.

我们谨慎的合作策略本质上是在发展区分自我与他人的能力。如果对手握手的方式正确，那么它就是自我。如果没有，它就是他人。因此，在这个系统中，合作是通过让策略与自己对抗而产生的，这很容易解决合作困境。这种新的合作途径是亲属选择的一个有趣变体，系统中出现合作是因为代理共享一个共同的遗传基础。在这里，亲属的概念自发出现握手的功能提供了另一种群体凝聚力。沟通可以实现这种凝聚力，这一观点是一个诱人的假设。它表明，沟通的出现可能是社会系统合作并最终生存的关键途径。

Our cautiously cooperative strategies are, in essence, evolving the ability to distinguish self from other. If an opponent gives the proper handshake, then it is considered self. If not, it is other. Thus, cooperation emerges in this system by having strategies play against themselves, which easily solves the cooperative dilemma. This new route to cooperation is an interesting variant on kin selection, whereby cooperation emerges in a system because the agents share a common genetic basis. Here, the notion of kin spontaneously arises as a function of the handshake that provides an alternative sense of group cohesion. The notion that communication allows such cohesion is a tempting hypothesis. It suggests that the emergence of communication could be a key path to cooperation in social systems and ultimately to survival.

竞争会让你的境况稍微好一点，而合作会让你的境况大大好一点，这一观察结果可能是社会世界的一个基本属性。不幸的是，这些世界的另一个基本属性是个人激励往往倾向于竞争而不是合作。话虽如此，我们对两个截然不同的系统的研究给了我们一线希望。通过聚焦复杂系统研究中使用的各种视角，从对巴厘岛稻农宗教习俗的细致人类学研究到对人工进化和抽象自动机理论驱动的计算生态系统的分析，我们发现即使在看似有利于竞争的系统中，合作也可以出现并维持。

The observation that being competitive makes you slightly better off while being cooperative makes you remarkably better off may be a fundamental property of social worlds. Unfortunately, another fundamental property of these worlds is that individual incentives tend to favor competition over cooperation. That being said, our exploration of two dramatically different systems gives us a ray of hope. By focusing the various lenses used in the study of complex systems, ranging from careful anthropological work on the religious practices of Balinese rice farmers to the analysis of computational ecosystems driven by artificial evolution and abstract theories of automata, we find that cooperation can arise and be maintained, even in systems that seemingly favor competition.

或许，手与心的结合，比我们想象的还要容易。

Perhaps the joining of hands and hearts is easier than we imagine.

十一

eleven

从石头到沙子：自组织临界性

From Stones to Sand: Self-Organized Criticality

没有什么是建立在石头上的；一切都是建立在沙子上的。但我们必须把沙子当成石头来建造。

Nothing is built on stone; all is built in sand. But we must build as if the sand were stone.

—豪尔赫·路易斯·博尔赫斯

—Jorge Luis Borges

赫我们从一堆沙子开始，而不幸的是，最终只剩下一堆沙子。我们经常观察到，复杂的系统在发展出美丽而看似坚固的结构后，可能会在瞬间崩溃。想想你的身体，它是数十亿个细胞的集合，每个细胞相互作用，形成一个可识别的、充满活力的你。然而，所有这些相互作用，你所是的一切和可能的一切，都可能在几分钟内停止，比如说，你的心脏受到了一次不适当的冲击。或者想想玛雅文明，在古典时期，一个充满活力的中美洲文化突然崩溃。复杂系统是否天生就具有某种不可避免地脆弱性，以致崩溃？

Here we begin with a pile of sand and, alas, end with one. We often observe that complex systems, after having developed a beautiful and seemingly robust structure, can collapse in an instant. Consider your body, a collection of billions of cells, each interacting and forming a recognizable and vital you. Yet all of those interactions, all that you are and could be, can cease in only a few minutes if, say, you experience a misplaced shock to your heart. Or consider a civilization such as the Maya in their Classic period, in which a vibrant Mesoamerican culture suddenly falls apart. Is there something innate about complex systems that demands an inescapable vulnerability to collapse?

为了探究这个问题，让我们在一张空桌子上随机撒上几粒沙。起初，沙粒落下时会停留在原地。随着时间的推移，偶尔会有一粒沙落在另一粒沙之上，只要新的高度不比周围沙粒高太多，它就会保持平衡。随着沙子不断堆积，最终会达到一个点，一粒沙无法再在它落下的地方保持平衡，然后随着沙粒滚落到相邻的沙粒上，就会发生小规模的崩塌。由于桌子上的沙粒很少，这种翻滚会导致不断增长的沙堆略微发生位移。然而，随着沙子继续在桌子上堆积，翻滚开始导致邻近位置的不平衡，从而导致新的翻滚和更大的崩塌，甚至可能达到一些沙子从桌子边缘掉落的程度。

To explore this question, let’s randomly sprinkle grains of sand on top of an empty table. At first, as the grains fall, they stay where they land. With time, an occasional grain lands on top of another grain, and as long as the new height is not much higher than that of the surrounding grains, it will balance. As the sand continues to pile up, we eventually reach a point where a grain can no longer balance where it falls, and a little avalanche ensues as the grain tumbles onto its neighbor. With few grains on the table, such tumbles result in a slight displacement of the ever-growing pile. However, as the sand continues to mound on the table, tumbles begin to cause imbalances at neighboring locations, resulting in new tumbles and a larger avalanche, perhaps even to the point where some sand falls off the edge of the table.

这种沙堆的行为方式构成了物理学家 Per Bak 开发的自组织临界性模型的核心。有时，一粒沙粒落下除了回到它落下的地方外，几乎没有其他影响。有时，沙粒会引发雪崩，引发连锁反应，使更多的沙粒滚落到沙堆上。事实上，所有可能大小的雪崩都遵循一个明确指定的概率分布（又一个幂律），表征了该系统的行为（见图 11.1）。

How such sand piles behave forms the core of a model of self-organized criticality developed by the physicist Per Bak. Sometimes a falling grain has little impact other than to add itself to the spot where it landed. At other times the grain begins an avalanche that triggers a chain reaction of additional grains tumbling across the pile. Indeed, avalanches of all possible sizes, following a well-specified probability distribution (yet another power law), characterize this system’s behavior (see Figure 11.1).

图 11.1：随机添加沙子最终会形成一个自组织临界系统。一旦系统达到这一临界状态，额外的沙子就会导致任何规模的雪崩，其特征是幂律分布。（作者拍摄。）

Figure 11.1: Random additions of sand eventually result in a self-­organized critical system. Once the system achieves this critical state, additional sand can result in avalanches of any size, characterized by a power law distribution. (Photograph by the author.)

在我们倒沙子的实验过程中，我们可以随时停下来，观察桌子上任何位置的情况。在每个位置，沙子堆都是要么处于亚临界状态（即，添加一粒沙子只会使其高度增加一米），要么处于临界状态（即，它摇摇欲坠，添加一粒沙子就会使其滚落到相邻的位置）。我们添加的每一粒沙子，发生的每一次滚落，都在不断将系统推向临界状态。有时，沙堆的大片区域处于平衡状态，因此添加一粒沙子就会导致整个区域发生雪崩。在雪崩摧毁了沙堆之后，系统已经足够放松，以至于新添加的沙子要么留在原地，要么只导致小范围的局部雪崩，这些雪崩很快就会被亚临界的邻居吸收。总体而言，我们观察到长时间的相对局部动荡，这种动荡日益使系统走向大范围的临界状态，为哪怕是一个小事件引发另一场大范围的雪崩奠定了基础。

At any given time during our sand-pouring experiment, we could pause and take stock of the conditions at any location on the table. At every location, the pile is either subcritical (that is, adding a grain will just increase its height by one) or critical (that is, it’s teetering in such a way that the addition of a single grain of sand will cause it to tumble onto a neighboring spot). Every grain of sand we add, every tumble that occurs, is continually pushing the system toward a critical state. At times, large swaths of the pile are poised so that the addition of a single grain of sand will cause an avalanche across the entire area. After that avalanche has devastated the pile, the system has relaxed enough so that new additions of sand either stay where they land or result in only small, localized avalanches that are quickly absorbed by subcritical neighbors. Overall, we observe long periods of relatively localized turmoil that increasingly drive the system toward widespread criticality, setting the stage for even a small event to trigger another widespread avalanche.

驱动此类系统的一种逻辑是永恒不变的。上文中，我们假设了一个简单的物理现象，沙粒行为良好，当它们堆积得太高时，会因重力而倾倒。即使我们通过使沙粒更不规则或改变重力来修改物理现象，也会出现类似的行为。在这些新条件下，系统仍会趋向临界状态。因此，无论我们用地球上的沙滩还是月球上的尘埃进行实验，系统的自组织临界性仍然是一个基本的、新兴的特征。

There is a relentless logic that drives such systems. Above, we assumed a simple physics with nicely behaved grains of sand that topple due to gravity when they pile too high. Even if we modify the physics by making the grains more irregular or by altering the force of gravity, similar behavior emerges. Under these new conditions, the system is still driven toward critical states. So whether we experiment with beach sand here on earth or dust on the moon, the self-organized criticality of the system remains a fundamental, emergent feature.

虽然沙堆主要由简单的物理学组成，但其他系统可能由其他机制驱动。例如，社会系统的临界性可能取决于法律法规或金融风险等特征。法律法规有时对社会行为的影响可能很小。但随着代理环境的变化，政策开始具有约束力，迫使代理进入临界状态，即使是小事件也可能引发大规模反应。因此，我们可能会看到社会各阶层起来反对政府的税收和财政政策，也许一开始只是形成类似茶党的地方运动，但有时会引发广泛的社会反抗。或者考虑银行和投资系统，其中各种机构试图通过利用资产和承担风险来最大化收益。随着时间的推移，这些系统可能会进入关键状态，即使是很小的变化，也许是一家银行无力偿还一笔贷款，也可能导致大规模的崩塌，因为失败会导致失败。

While the sand pile is dominated by simple physics, other systems may be driven by other mechanisms. For example, criticality in social systems might depend on features such as laws and regulations or financial risk. Laws and regulations may have little impact on social behavior at times. But as the circumstances of agents change, policies begin to bind, forcing agents into critical states where even small events can trigger large responses. Thus, we might see segments of society rise up against the government’s taxation and fiscal policy, perhaps at first just forming local Tea Party–like movements, but on occasion triggering widespread social revolts. Or consider the banking and investment system, where various institutions try to maximize their returns by leveraging their assets and taking on risk. Over time, these systems can enter critical regimes where even small changes, perhaps the inability of one bank to repay a single loan, can result in a large avalanche as failure begets failure.

在物理系统中，临界性的驱动因素（如重力）是外生的，而在社会系统中，它们往往是内生的。税率和银行获准行使的杠杆率等社会因素由政府控制，通常是通过某种政治程序。政治参与者往往有动机改变这些政策，从而可能改变临界性的关键决定因素。

While in physical systems the drivers of criticality (such as gravity) are exogenous, in social systems they are often endogenous. Social elements such as tax rates and the amount of leverage banks are allowed to exercise are under the control of the government, typically through some political process. Political actors often have incentives to alter such policies in ways that might change the key determinants of criticality.

想象一下古典时期的玛雅城市。城市周围都是农民，他们必须向政府纳税，要么交出一部分农作物，要么提供劳动力。作为回报，农民会得到城市的服务，比如保护、治理，以及一些保险，以防他们的农作物歉收。在低税率的情况下，农民们很高兴，因为他们缴纳的税款比他们得到的服务还要多。随着税收的增加，农民对他们必须做出的权衡越来越不满。在某个时候，情况可能会变得非常糟糕，农民可能会反抗或搬到其他地方。

Consider a Classic-period Mayan city. The city proper is surrounded by farmers who must pay a tax to the government, either by turning over a share of their crops or by providing labor. In return, the farmers receive services from the city, such as protection, governance, and some insurance in case their crops fail. At low tax rates, the farmers are happy, because the amount they pay in taxes is more than compensated for by the services they receive. As the taxes are raised, the farmers become increasingly disgruntled with the trade-off they must make. At some point, things may become so bad that a farmer might rebel or move elsewhere.

假设我们的玛雅政府像大多数政府一样，宁愿增加收入也不愿减少收入，也许是因为总有建造更精致的寺庙的需求。随着政府提高税率，它开始将系统推向临界状态。每个农民都在不断做出选择，权衡留在当前位置的好处和必须缴纳的税款。他会考虑自己在改善田地方面的投资、朋友圈、与该地的祖先关系等等。随着税率的上升，留下的好处和离开的成本之间的不平衡逐渐减少，农民被推向更接近临界状态，即使是一个很小的变化——一些恶劣的天气或失去一个合作的邻居，更不用说新的政府要求——也可能导致农民离开。

Suppose our Mayan government, like most governments, prefers more revenue rather than less, perhaps because there is always a demand to build more elaborate temples. As the government raises tax rates, it starts to push the system closer to criticality. Every farmer is continually making a choice, weighing the benefits of staying at his current location against the tax he must pay. He’ll consider his investments in improving the fields, his network of friends, his ancestral ties to the place, and so on. As the tax rate rises, the imbalance between the benefits of staying and the costs of leaving lessens, and the farmer is pushed closer to a critical state where even a small change—some bad weather or the loss of a cooperative neighbor, let alone a new government demand—could cause the farmer to up and leave.

如果农民决定离开，我们会看到类似沙堆的影响。一方面，农民的田地现在处于休耕状态，只需要很少的投资就可以投入生产，可能会被别人接管。在这里，离开的农民就像一粒沙子，在沙堆中形成一个亚临界孔洞。另一方面，当农民离开时，他可能会引发邻居们也离开。毕竟，邻居们失去了一个重要的社会联系，这个联系提供了友谊和合作，而通过搬家，人们不再对重新安置祖先的骨头感到忌讳。后一种情况就像一粒沙被其他处于临界状态的沙粒包围着。

If a farmer decides to leave, we see impacts that resemble those in our sand pile. On one hand, the farmer’s field, now fallow and needing minimal investment to put it into production, might simply be taken over by someone else. Here, the departing farmer is like a grain of sand forming a subcritical hole in the pile. Alternatively, when the farmer leaves he might trigger his neighbors to leave as well. After all, the neighbors lost an important social connection who provided friendship and cooperation, and who by moving lessened the taboo against relocating the bones of one’s ancestors. This latter situation is much like a grain of sand surrounded by other grains all in a critical state.

与物理系统不同，社会系统可能体现出额外的内生力量，这些力量可能会加速其临界性。例如，玛雅农民迁徙带来的直接生产损失可能迫使政府增加对剩余农民的税收。这将导致整个系统临界性进一步增加。事实上，这种内生驱动力导致临界性增加可能是社会治理，因为政府在追求其目标时往往会推动公民采取行动。一旦系统变得危急，即使是微不足道的外部事件或政策变化也会引发整个系统的反应。

Unlike physical systems, social systems are likely to embody additional endogenous forces that could accelerate their criticality. For example, the immediate loss of production from the relocating Mayan farmer may force the government to increase its taxation on the remaining farmers. This will cause a further increase in system-wide criticality. Indeed, such endogenous drives toward increased criticality may be a natural outcome of social governance, as governments in pursuit of their goals tend to push citizens toward action. Once the system becomes critical, even trivial external events or policy changes can provoke system-wide reactions.

自组织临界性的概念可能为涉及快速崩溃和变化的社会现象提供一些必要的见解。古典时期玛雅城市的迅速废弃可能是由多年的社会政策所预示的，这些政策迫使系统进入临界状态。一旦社会处于这种状态，沙堆的动态就会接管。任何社会系统都会不断受到看似微不足道的事件的干扰，例如恶劣天气、统治者的失误等等。这些扰动通常不会产生明显的后果。也许，偶尔，一个农民和一两个邻居决定离开并在其他地方开展业务，但仅此而已。然而，这样的行动和反应会慢慢地流经系统，不可避免地将其推向临界状态。一旦到了那里，对系统的一个看似轻微的冒犯可能会引发大规模的雪崩。

The idea of self-organized criticality may provide some needed insight into social phenomena involving rapid collapse and change. The rapid abandonment of Mayan cities in the Classic period could have been presaged by years of social policy that forced the system into a critical state. Once the society was in this state, the dynamics of the sand pile took over. Any social system is continually perturbed by seemingly insignificant events such as bouts of bad weather, missteps by the ruler, and so on. These perturbations usually have few noticeable consequences. Perhaps, on occasion, a farmer and maybe a neighbor or two decide to leave and set up operations elsewhere, but nothing much more than that. Yet such actions and reactions slowly flow through the system and inexorably drive it to a critical state. Once there, a seemingly minor affront to the system can trigger a large-scale avalanche.

2010 年 12 月 17 日，突尼斯街头小贩穆罕默德·布瓦吉吉 (Mohamed Bouazizi) 为抗议当局多年来的骚扰而自焚。引发他抗议的事件是一名市政官员没收了他用来称重农产品的秤，公开羞辱了他。布瓦吉吉试图向州长投诉，但州长拒绝见他。这导致他最终采取了自杀行为。

On December 17, 2010, a Tunisian street vendor, Mohamed Bouazizi, set himself on fire to protest years of harassment by authorities. The event that triggered his protest was a municipal official publicly humiliating him by confiscating the scale he used to weigh his produce. Bouazizi tried to complain to the governor, but the governor refused to see him. This led him to the act that would eventually take his life.

阿拉伯之春由此开始，突尼斯一个乡村小镇的摊贩被没收，引发了一波骚乱，从突尼斯蔓延到阿尔及利亚、黎巴嫩、约旦、毛里塔尼亚、苏丹、阿曼、沙特阿拉伯、埃及、也门、伊拉克、巴林、利比亚、科威特、摩洛哥、西撒哈拉、叙利亚和以色列边境城镇。迄今为止，这场骚乱导致了一系列革命，导致政府发生剧烈变动、严厉镇压和外交手段的运用。这些事件对世界历史进程的全面影响可能非常重大，但目前还很难理解。

Thus began the Arab Spring, where the confiscation of a vendor’s scale in a rural Tunisian town started a wave of unrest that rippled outward from Tunisia into Algeria, Lebanon, Jordan, Mauritania, Sudan, Oman, Saudi Arabia, Egypt, Yemen, Iraq, Bahrain, Libya, Kuwait, Morocco, Western Sahara, Syria, and Israel’s border towns. The outcome to date is a number of revolutions resulting in dramatic changes in governments, harsh crackdowns, and diplomatic maneuvering. The full impact of these events on the course of world history will likely be significant, but it’s hard to fathom at this stage.

人们可以很容易地假设一些力量，比如不满的公民或独裁统治者的命令，可以迫使社会陷入危机状态。此外，当一个公民被逼到决定抗议的地步时，这增加了附近的人也参与抗议的可能性。这些国家已经以各种形式发生了一段时间的抗议，但大多数抗议活动都是局部的。尽管如此，他们一直在悄悄地把系统推向更危急的状态。一旦系统进入这种状态，即使是一个无关紧要的行为也可能引发大规模的变化，而我们才刚刚开始了解其后果。虽然这种假设是推测性的，但人们可以通过在各种数据流（如 Twitter）中寻找日益严重的危机迹象来测试它，这些数据流很可能既捕捉到了这些事件，又促成了这些事件。

One can easily postulate forces, such as unhappy citizens or the dictates of an autocratic ruler, that could force a society into a critical state. Moreover, when one citizen is pushed so far that he decides to protest, this increases the likelihood that those nearby might take up the protest as well. Protests in various guises had been occurring in these countries for some time, but most of these efforts were quite localized. Nevertheless, they had been quietly driving the system to a more critical state. Once the system entered such a state, even an inconsequential act could trigger large-scale change, the consequences of which we are only starting to grasp. While such a hypothesis is speculative, one could test it by looking for the signatures of growing criticality in the various data feeds, such as Twitter, that may well have both captured and contributed to these events.

自组织临界性是一种有趣的复杂性形式，其中系统的小部分在局部相互作用相互影响，由一个非常简单的规则来控制变化。随着时间的推移，系统会脱离特定的局部规则，其整体行为由所有规模的雪崩特征模式主导。大多数雪崩都很小，但偶尔也会有一场雪崩席卷整个系统。当全球事件发生时，我们希望引起全球性原因。但自组织临界性的教训是，系统背后存在着力量，即使是通常无关紧要的小事件也会产生巨大影响。

Self-organized criticality is an interesting form of complexity where small pieces of the system interact locally with one another, mediated by a very simple rule governing change. Over time, the system abstracts itself away from the particular local rule, and its global behavior is dominated by a characteristic pattern of avalanches at all scales. Most of these avalanches are small, but on rare occasions one encompasses the entire system. When global events occur, we want to invoke global causes. But the lesson from self-organized criticality is that there are forces underlying systems such that even small events, normally inconsequential, can have huge impacts.

只需轻轻一碰，我们的世界就会从石头变成沙子。

At the slightest touch, our world can go from stones to sand.

十二

twelve

从中子到生命：复杂的三位一体

From Neutrons to Life: A Complex Trinity

西方与东方

As West and East

在所有的平面地图中——我也是其中之一——都是一体，

In all flatt Maps—and I am one—are one,

所以死亡确实影响复活。

So death doth touch the Resurrection.

—约翰·多恩，《在我病痛中，向上帝，我的上帝，献上赞美诗》

—John Donne, “Hymn to God, My God, in My Sickness”

哦1945 年 7 月 16 日，原子时代开始。山区战争时间凌晨 5:29 刚过，在偏远的 Jornada del Muerto 盆地（新墨西哥州南部的沙漠，西班牙征服者恰当地将其命名为“死人一天的旅程”），曼哈顿计划测试了一个内爆式钚装置，释放出约 20 千吨 TNT 炸药当量。这次测试由该项目的科学领导人主持，J. 罗伯特·奥本海默的代号为“三位一体”，显然源自奥本海默朗读的两首约翰·多恩的诗：本章开头的《赞美上帝》和《击碎我的心，三位一体的上帝》。三周后，一枚基于未经测试但更简单的设计、使用铀 235 的原子弹被投掷在日本广岛。三天后，一枚基于“三位一体”设计的装置被投掷在长崎。此后不久，日本投降，第二次世界大战结束。

On July 16, 1945, the atomic age began. At just past 5:29 a.m. Mountain War Time, in the remote Jornada del Muerto basin (a desert in southern New Mexico aptly named by Spanish conquistadors for its “single day’s journey of the dead man”), the Manhattan Project tested an implosion-­initiated plutonium device that released the equivalent of around twenty kilotons of TNT. The test, conducted under the auspices of the project’s scientific leader, J. Robert Oppenheimer, was code-named Trinity, apparently derived from Oppenheimer’s reading of two John Donne poems: “Hymn to God,” which opens this chapter, and “Batter my heart, three person’d God.” Three weeks later, an atomic bomb based on an untested but simpler design using uranium-235 was dropped on Hiroshima, Japan. Three days after that, a device based on the Trinity design was dropped on Nagasaki. Shortly thereafter, Japan surrendered, ending World War II.

核反应，无论是用于民用电力还是用于核弹，都依赖于相互作用。在一种反应中，高能中子可能会与附近的原子核发生碰撞，也许会导致裂变事件，从而释放出一些能量，甚至释放出更多高能中子。请注意“可能”和“也许”这两个词的使用。机会在这种系统中起着重要作用。如果中子产生中子，就有可能将质量转化为能量，就像爱因斯坦著名的E = m c 2一样。根据这种转化的速度，我们要么获得导致无碳民用电力生产的变暖，要么获得核爆炸的破坏力。考虑到原子所固有的潜在能量，战争开始时人们对了解这种原子尺度上发生的复杂相互作用有着浓厚的兴趣，这并不奇怪。这种相互作用体现了复杂三位一体的第一个分支，它将我们引向复杂自适应系统的基本定理。

Nuclear reactions, whether used for civilian power or for nuclear bombs, rely on interactions. In one type of reaction, energetic neutrons potentially collide with nearby nuclei, perhaps resulting in a fission event that releases some energy and even more energetic neutrons into the mix. Note the use of the words “potentially” and “perhaps.” Chance plays an important role in such systems. If neutrons beget neutrons, there is the potential to transform mass into energy à la Einstein’s famous E = mc2. Depending on the speed of that transformation, we can get either warming leading to the carbon-free generation of civilian power or the destructive force of a nuclear blast. Given the potential energy inherent in an atom, it is not surprising that at the start of the war there was an intense interest in understanding the complex interactions that take place at this atomic scale. Such interactions embody the first branch of a complex trinity that leads us to a fundamental theorem about complex adaptive systems.

我们三位一体的第二个分支始于宾夕法尼亚大学摩尔电气工程学院决定制造一种名为电子数字积分计算机的秘密新设备。它被称为 ENIAC，是第一台可编程电子计算机，是信息时代的里程碑式发展。物理学家约翰·莫奇利向位于马里兰州阿伯丁试验场的美国陆军弹道研究实验室提出了制造 ENIAC 的初步建议。莫奇利在遇到一群妇女（当时被称为“计算机”）后，受到启发，找到了一种更好的方法来生成弹道射击表，她们在桌上计算器上制作出这样的表格。莫奇利和工程师 Presper Eckert 负责 ENIAC 项目，最终开发出一台重达 30 吨的电子计算机，需要 1,800 平方英尺的占地面积、17,500 个真空管和数量惊人的焊点。

The second branch of our trinity begins with a decision to build a secret new device called the Electronic Numerical Integrator and Computer at the University of Pennsylvania’s Moore School of Electrical Engineering. Called the ENIAC, it was the first programmable electronic computer, and it was a milestone development in the information age. The initial proposal to build ENIAC was made to the United States Army’s Ballistics Research Laboratory at Aberdeen Proving Ground in Maryland by the physicist John Mauchly. Mauchly was inspired to find a better way to generate ballistic firing tables after encountering a group of women—known at the time as “computers”—literally cranking out such tables on desk calculators. Mauchly and an engineer, Presper Eckert, took charge of the ENIAC program, resulting in the eventual development of a thirty-ton electronic computer requiring 1,800 square feet of floor space, 17,500 vacuum tubes, and an astounding number of solder joints.

约翰·冯·诺依曼曾担任阿伯丁大学的顾问。在了解了 ENIAC 后，他意识到 ENIAC 可能会被重新用于帮助解决“热核问题”——即基于核聚变而非核裂变的炸弹——由物理学家爱德华·泰勒领导的冯·诺依曼在洛斯阿拉莫斯的一些同事正在研究。1945 年 3 月，冯·诺依曼、尼克·梅特罗波利斯和斯坦·弗兰克尔访问了摩尔学院，并开始敲定计划，建立一个将在 ENIAC 上运行的热核反应计算模型。

John von Neumann was a consultant to Aberdeen. Upon learning about ENIAC, he realized that it might be repurposed to help solve the “thermonuclear problem”—that is, a bomb predicated on nuclear fusion rather than fission—being pursued by some of von Neumann’s Los Alamos colleagues led by physicist Edward Teller. In March 1945, von Neumann, Nick Metropolis, and Stan Frankel visited the Moore School and began to finalize plans for building a computational model of a thermonuclear reaction that would be run on ENIAC.

虽然战争在他们完成工作之前就结束了，但到 1946 年春天，梅特罗波利斯和弗兰克尔已经与洛斯阿拉莫斯的一个高层小组讨论了 ENIAC，并向他们介绍了他们的计算和结论，其中包括冯·诺依曼、泰勒、洛斯阿拉莫斯主任诺里斯·布拉德伯里、恩里科·费米和斯坦·乌拉姆。尽管模型很简单，但结果令人鼓舞。在复杂系统史上，这代表了使用电子计算来理解具有严重现实影响的复杂相互作用的重要里程碑。

While the war ended before they had completed their work, by the spring of 1946 Metropolis and Frankel had discussed ENIAC with and presented their calculations and conclusions to a high-level group in Los Alamos, including von Neumann, Teller, Los Alamos director Norris Bradbury, Enrico Fermi, and Stan Ulam. Although the model was simple, the results were encouraging. In the annals of complex systems, this represents an important milestone in the use of electronic computation to understand complex interactions with serious, real-world implications.

受到 Metropolis 和 Frankel 成果的启发，Ulam 意识到可以使用电子计算机实现许多繁琐但功能强大的统计抽样技术。Ulam 与冯·诺依曼讨论了这个想法，后者向洛斯阿拉莫斯理论部门负责人提出了这个想法。该方法使用计算生成的随机性来解决复杂问题，它标志着后来被称为蒙特卡罗方法的正式开始。a (这个名字是由 Metropolis 建议的，它“与 Stan [Ulam] 的一位叔叔向亲戚借钱，因为他‘必须去’”这一事实不无关系。到 20 世纪 40 年代末，蒙特卡罗方法在各种研讨会的推动下，已成为一种公认的科学工具。

Inspired by the results of Metropolis and Frankel, Ulam realized that a number of cumbersome but powerful statistical sampling techniques could be implemented using electronic computers. Ulam discussed this idea with von Neumann, who broached it with the leader of the Los Alamos Theoretical Division. The approach used computationally generated randomness to solve complex problems, and it marks the formal beginning of what has come to be known as the Monte Carlo method.a (The name was suggested by Metropolis, and it was “not unrelated to the fact that Stan [Ulam] had an uncle who would borrow money from relatives because he ‘just had to go to Monte Carlo.’”) By the late 1940s the Monte Carlo method, promoted by various symposia, had become an accepted scientific tool.

蒙特卡罗方法在 1953 年发表的一篇开创性的论文《快速计算机的状态方程计算》中发挥了关键作用。这篇论文有五位作者：Metropolis、Arianna 和 Marshall Rosenbluth 以及 Augusta 和 Edward Teller。这篇论文的核心是“一种适用于快速电子计算机的通用方法，用于计算任何可被视为由相互作用的单个分子组成的物质的性质。”这被称为 Metropolis 算法。

Monte Carlo methods played a key role in a groundbreaking paper, “Equation of State Calculations by Fast Computing Machines,” published in 1953. The paper had five authors: Metropolis, Arianna and Marshall Rosenbluth, and Augusta and Edward Teller. At the heart of the paper was “a general method, suitable for fast electronic computing machines, of calculating the properties of any substance which may be considered as composed of interacting individual molecules.” This has become known as the Metropolis algorithm.

这篇论文重点讨论了相互作用的粒子在空间中的分布情况。每个粒子都会与其他粒子相互作用，我们可以计算出任何给定配置的总能量。这篇论文提出的挑战是找到该系统最可能的配置。

The paper focused on the question of how interacting particles will be distributed in space. Each particle interacts with the others, and we can calculate the overall energy for any given configuration. The challenge posed in the paper was to find the most likely configurations for this system.

解决这个问题的一种方法是将粒子建模为硬币，将空间建模为桌面。我们可以随机地将硬币扔到桌子上，计算所得配置的能量，就好像硬币代表原子的位置一样，然后重复。经过多次重复，我们将开始了解系统可能的能量状态的分布。可惜的是，这种方法的问题在于，我们将花费大量精力来生成不太可能出现的配置。在物理学中，假设系统会寻找能量较低的配置，而很多我们的随机抛掷将产生不太可能观察到的高能量配置。

One approach to solving this problem would be to model particles as coins and space as a tabletop. We could randomly toss coins on the table, calculate the energy of the resulting configuration as if the coins represented the position of atoms, and repeat. After numerous repetitions, we would begin to get a sense of the distribution of possible energy states for the system. Alas, the problem with this approach is that a lot of our effort will be spent on generating configurations that are not all that likely to appear. In physics, it is assumed that systems seek out lower-energy configurations, and a lot of our random tosses would result in high-energy configurations that we are not likely to observe.

Metropolis 及其同事 提供了一种寻找最可能配置的替代解决方案，并且该解决方案中体现的技术对于现代统计方法以及理解复杂自适应系统（如我们将在三位一体的最后一个分支中看到的那样）都具有深远的影响。

Metropolis and colleagues provided an alternative solution for finding the most-likely configurations, and the technique embodied in this solution has profound implications both for modern statistical methods and, as we will see in the last branch of our trinity, for understanding complex adaptive systems.

从表面上看，Metropolis 及其合著者提出的解决方案 似乎非常简单。首先，从随机得出的硬币配置开始，并将其标记为现状。接下来，考虑通过采用现状并使用由提议分布驱动的随机过程随机移动其中一枚硬币而产生的新硬币配置。现在，我们计算与现状和新配置的结果配置相关的一些兴趣度量（在上述系统中，与硬币位置相关的原子相互作用产生的能量）。然后，我们使用接受函数来决定这两种配置中的哪一种将成为新的现状。如果候选配置优于先前的现状，则立即接受该候选配置作为新的现状。如果候选配置较差，那么它取代先前现状的可能性与它们各自的兴趣度量成正比。候选配置越不如先前的现状，它成为新现状的可能性就越小。

The solution suggested by Metropolis and his coauthors seems remarkably simple on its face. First, begin with a randomly derived configuration of the coins and label this the status quo. Next, consider a new configuration of the coins generated by taking the status quo and randomly moving one of the coins by a small amount using a random process driven by a proposal distribution. We now calculate some measure of interest tied to the resulting configurations (in the above system, the amount of energy resulting from the interactions of atoms tied to the locations of the coins) for both the status quo and the new configuration. We then use an acceptance function to decide which of these two configurations will become the new status quo. If the candidate configuration is superior to the previous status quo, the candidate is accepted immediately as the new status quo. If the candidate configuration is inferior, then the likelihood that it replaces the previous status quo is proportional to their respective measures of interest. The more inferior the candidate is to the previous status quo, the less likely it will become the new status quo.

该算法通过使用当前现状迭代上述步骤来进行。令人惊讶的是，如果我们跟踪该算法随时间访问的各种配置，我们会发现这些配置会收敛到感兴趣的度量所依据的精确分布。也就是说，系统将在那些具有最高兴趣度量的配置中花费相对较多的时间。就上面的粒子系统而言，如果我们运行算法一段时间，然后随机抽样现状，我们往往会发现系统处于低能量状态。

The algorithm proceeds by iterating the steps above using the current status quo. Amazingly, if we track the various configurations that this algorithm visits over time, we find that these configurations converge on the exact distribution underlying the measure of interest. That is, the system will spend relatively more time in those configurations that have the highest measure of interest. In the case of our particle system above, if we run the algorithm for a while and then randomly sample the status quo, we will tend to find the system in low-energy states.

直观来看，该算法的行为是有道理的，因为我们的接受标准倾向于将系统引导到具有较高关注度的区域，同时避开具有较低值的区域。话虽如此，考虑到该算法从未使用任何有关底层分布的全局信息，系统与关注度相关的分布完全一致这一事实更加令人惊讶。

Intuitively, the algorithm’s behavior makes sense, as our acceptance criteria tend to direct the system into areas with higher measures of interest while avoiding areas with lower values. That being said, the fact that the system perfectly aligns with the distribution tied to the measure of interest is much more surprising, given that the algorithm never uses any global information about the underlying distribution.

无论算法的行为看起来多么神奇，我们都可以数学地理解它。第一个关键点是算法总是使用现有的现状作为锚点。现状包含一些重要信息，因此算法不是随机地搜索可能的配置，否则会导致非常不同的结果。例如，我们可以通过简单地计算全年下雨的天数，然后使用这个比例作为我们对任何一天降雨的预测来预测天气。或者，我们可以计算一天下雨的可能性假设前一天下雨，则预测某一天的天气。正如您可能想到的，后一种方法会给我们一组非常不同的概率，并且对于天气而言，预测会更加准确，因为今天的天气可以很好地预测明天的天气。

However miraculous the algorithm’s behavior may seem, it is possible to understand it mathematically. The first key piece is that the algorithm always uses the existing status quo as an anchor. The status quo embodies some important information, and thus the algorithm is not just randomly searching across possible configurations, which would result in a very different outcome. For example, we can forecast the weather by simply calculating the number of days that it rains throughout the year and then using this proportion as our prediction of rain on any given day. Alternatively, we could calculate the likelihood of rain on a particular day given that it rained on the previous day. As you might suspect, the latter approach gives us a very different set of probabilities and, in the case of weather, a much more accurate prediction, since the weather today is a good predictor of the weather tomorrow.

一个事件（例如昨天的天气或现状配置）可能会影响下一个事件发生概率的想法可以追溯到 20 世纪初的俄罗斯数学家安德烈·安德烈耶维奇·马尔可夫，他开发了许多关于这些系统的重要结果，这些结果现在被称为马尔可夫链。1953 年，Metropolis 及其同事的论文 利用马尔可夫的一些想法创建了一类新的算法，称为马尔可夫链蒙特卡罗 (MCMC) 方法。

The idea that one event—say, yesterday’s weather or the status quo configuration—might influence the probability of the next event goes back to the Russian mathematician Andrey Andreyevich Markov in the early 1900s, who developed a number of important results about these systems that are now known as Markov chains. The 1953 paper of Metropolis and colleagues used some of Markov’s ideas to create a new class of algorithms called Markov chain Monte Carlo (MCMC) methods.

如果控制从一个状态到另一个状态的转换的概率使得从每个状态到其他每个状态成为可能（尽管不一定一次移动），那么马尔可夫链被称为遍历链（或不可约链）。如果这样的转换在 n 步或更多步之后始终可能，则该链被称为规则链。b在 MCMC 算法中，很容易为下一个配置选择一个提议分布，以保证生成的马尔可夫链是规则的。通常，有一个对称分布也很有用度量提议分布（与原始 Metropolis 算法中一样）。这要求给定y时提议x的概率与给定x时提议y的概率相同。

If the probabilities that govern the transitions from one state to another make it possible to go from every state to every other state (though not necessarily in one move), then the Markov chain is known as ergotic (or irreducible). If such transitions are always possible after n or more steps, the chain is called regular.b In the MCMC algorithm, it is easy to choose a proposal distribution for the next configuration that will guarantee that the resulting Markov chain will be regular. Typically, it also is useful to have a symmetric proposal distribution (as was done in the original Metropolis algorithm). This requires that the probability of proposing x given y is identical to the probability of proposing y given x.

MCMC 算法由常规马尔可夫链驱动这一事实很有用，因为随着系统向前运行，这些链变得越来越良好。这样的系统会崩溃成一个非常良好的状态，其中在任何特定状态下找到它的概率是固定的，并且与系统从哪里开始无关。也就是说，如果我们运行 MCMC 算法足够长的时间，系统将开始以可预测的方式访问各种状态。以天气为例，无论今天的天气如何，如果我们等待足够长的时间，未来随机选择的一天下雨的概率将是固定的。然而，这些系统确实需要一定的磨合时间。虽然我们可以在任何地方启动系统，但链条需要一定的时间来忘记它从哪里开始并找到其更基本的行为。这到底需要多长时间对于适应具有重要意义。

The fact that MCMC algorithms are driven by a regular Markov chain is useful, as these chains become increasingly well behaved as the system runs forward. Such systems collapse into a very well-behaved regime where the probability of finding it in any particular state is fixed and independent of where the system started. That is, if we run our MCMC algorithm long enough, the system will start to visit the various states in a predictable way. In the case of weather, regardless of the weather today, if we wait long enough, the chance of rain on a randomly chosen day in the future will be fixed. These systems do, however, require a certain amount of burn-in time. While we can start the system anywhere, it takes the chain a certain amount of time to forget where it began and to find its more fundamental behavior. Exactly how long that takes has important implications for adaptation.

MCMC 卓越性能的第二个关键方面涉及接受标准。接受标准的选择是经过深思熟虑的，因为它保证算法收敛到我们感兴趣的度量所暗示的底层概率分布。这种收敛的奇怪之处在于，我们通常无法直接计算这个概率分布，因为它需要有关所有可能配置的信息系统，并且此类配置的数量通常非常大，以至于无法执行此计算。幸运的是，算法不需要直接执行这样的计算。保证所需收敛的充分条件是称为详细平衡的属性。详细平衡要求当系统收敛时，所产生的转换是可逆的，即从一种配置移动到另一种配置的平衡概率在任一方向上都是相同的。如果详细平衡成立，则系统收敛到驱动感兴趣度量的底层概率分布。

The second key aspect of the MCMC’s remarkable behavior involves the acceptance criteria. The choice of the acceptance criteria is made with careful forethought, as it guarantees that the algorithm converges to the underlying probability distribution implied by our measure of interest. The odd thing about this convergence is that we typically cannot calculate this probability distribution directly, as it requires information about all possible configurations of the system, and the number of such configurations is usually so large that performing this calculation is impossible. Fortunately, the algorithm doesn’t need to directly perform such a calculation. A sufficient condition that guarantees the needed convergence is a property known as detailed balance. Detailed balance requires that when the system converges, the resulting transitions are reversible in the sense that the equilibrium probability of moving from one configuration to another is the same in either direction. If detailed balance holds, then the system converges to the underlying probability distribution driving the measure of interest.

亚瑟·克拉克曾说过，“任何足够先进的技术都与魔法无异”，也许 MCMC 就是这样一种技术。通过一组非常简单的操作——随机创建一个取决于现状的候选配置，并可能用基于与两个配置的相对测量值相关的掷骰子结果的候选配置替换现状——我们创建了一个由更深层次的力量驱动的系统，这种力量以前是我们无法接近的，因为无法进行所需的计算。MCMC 方法彻底改变了科学界。特别是，这种算法对于贝叶斯统计的广泛应用是必不可少的，贝叶斯统计现在是一种无处不在的方法，它正在开启一个新的分析时代，其特点从有针对性的网络广告到无人驾驶汽车应有尽有。贝叶斯方法的核心是需要计算一些关键的概率分布。这些分布通常无法通过计算直接计算，但我们可以借助 MCMC 的魔力。

Arthur C. Clarke noted that “any sufficiently advanced technology is indistinguishable from magic,” and perhaps MCMC is one such technology. Through a very simple set of manipulations—randomly creating a candidate configuration contingent on the status quo and possibly replacing the status quo with that candidate configuration based on a roll of the dice tied to the relative measures of interest of the two configurations—we create a system that is driven by a much deeper force, one that was previously inaccessible to us given the impossibility of making the required calculations. MCMC methods have radically altered the scientific landscape. In particular, such algorithms are needed for the widespread application of Bayesian statistics, a now ubiquitous approach that is ushering in a new analytic age characterized by everything from targeted web ads to driverless cars. At the heart of Bayesian methods is the need to calculate some key probability distributions. Such distributions are often computationally impossible to calculate directly, but we can invoke the magic of MCMC.

这将我们带到了复杂三位一体的第三个分支，即前两个分支对于理解复杂自适应系统的意义。MCMC 算法最初开发的动力是找到一种简单的方法来揭示以前隐藏但至关重要的分布。在 Metropolis 及其同事的案例中，这是相互作用粒子系统的可能能量状态的分布。为了实现这一目标，算法的创建者开发了一组简单的迭代步骤来生成所需的候选。就像变魔术一样，这些简单的步骤足以揭示所需的分布。MCMC 算法对复杂自适应系统的意义更为深远。驱动自适应系统的机制（例如进化）与 MCMC 算法的关键元素有直接的类似性。简而言之，复杂自适应系统的行为就像是在实施 MCMC 算法一样。

This brings us to the third branch of our complex trinity, namely, the implications of the first two branches for understanding complex adaptive systems. The impetus for the original development of MCMC algorithms was to find a simple method that could reveal a previously hidden but vitally important distribution. In the case of Metropolis and colleagues, this was the distribution of the likely energy states for a system of interacting particles. To accomplish this goal, the creators of the algorithm developed a set of simple, iterative steps that generated the needed candidates. As if by magic, such simple steps are sufficient to uncover the desired distribution. The implications of MCMC algorithms are even more profound for complex adaptive systems. The mechanisms that drive adaptive systems, such as evolution, have direct analogs to the key elements of the MCMC algorithm. In short, a complex adaptive system behaves as if it were implementing a MCMC algorithm.

假设一个池塘里长满了睡莲，其中一片睡莲上有一只青蛙。我们假设，根据睡莲的位置，每片睡莲对青蛙来说都有一些内在价值，比如，青蛙在给定时间内可以抓到的飞虫数量（假设这种昆虫的供应不断更新）。假设青蛙的行为如下：每分钟它随机挑选一个相邻的睡莲，如果新睡莲上的昆虫数量大于如果当前 pad 上的昆虫数量为 1，则跳转到相邻 pad。否则，跳转到新 pad 的概率与两个位置的昆虫相对数量成比例。因此，相邻 pad 上的昆虫数量越接近当前 pad 上的昆虫数量，移动的机会就越大。

Consider a pond covered with lily pads, on one of which sits a frog. We assume that each lily pad, depending on its location, has some inherent value for the frog—say, the number of flying insects that the frog can snatch in a given time (assuming that the supply of such insects is constantly renewed). Suppose the frog behaves as follows: Every minute it randomly picks a neighboring lily pad, and if the number of insects at that new pad is greater than the number at the current pad, it jumps to the neighboring pad. Otherwise, it jumps to the new pad with a probability proportionate to the relative number of insects at the two locations. Thus the chance of moving will be higher the closer the number of insects at the neighboring pad is to the number at the current one.

显而易见，青蛙正处于 MCMC 算法之中。睡莲叶代表系统的各种状态，青蛙的位置标记着现状配置。当青蛙考虑随机选择的相邻睡莲叶时，它会从提议分布中抽取。青蛙决定跳到新睡莲叶（即创建新的现状）是通过 Metropolis 算法中使用的接受标准来实现的，如果新睡莲叶（状态）更好，则始终接受新睡莲叶（状态），如果新睡莲叶更差，则以与相对质量相关的概率接受它。

As might be apparent, the frog is in the midst of a MCMC algorithm. The lily pads represent various states of the system, and the location of the frog marks the status quo configuration. When the frog considers a randomly chosen neighboring lily pad, it is drawing from a proposal distribution. The frog’s decision to jump to the new pad (that is, to create a new status quo) is implemented via the acceptance criteria used in the Metropolis algorithm, always accepting the new pad (state) if it is better, and if it is worse, accepting it with a probability tied to the relative quality.

鉴于青蛙正在实施 MCMC 算法，我们可以轻松描述其长期行为。经过一定量的初始跳跃（即磨合时间）后，如果我们跟踪青蛙的位置，我们会发现它在任何特定睡莲上花费的时间等于该睡莲上发现的昆虫数量除以所有睡莲上昆虫的总数。这些分数加在一起，为我们提供了一个概率分布，描述了青蛙在未来某个时间出现在特定睡莲上的可能性。例如，如果我们有三个睡莲，第一个有 50 只昆虫，第二个有 30 只，第三个有 20 只，那么随着时间的推移青蛙有 50% 的时间待在第一个垫子上，有 30% 的时间待在第二个垫子上，有 20% 的时间待在第三个垫子上（见图 12.1）。

Given that the frog is implementing a MCMC algorithm, we can easily characterize its long-run behavior. After a certain amount of initial hopping (aka burn-in time), if we track the frog’s location, we will find that the amount of time it spends on any particular lily pad is given by the number of insects found at that pad divided by the total number of insects across all of the pads. These fractions, taken together, give us a probability distribution describing the likelihood of the frog being on a particular lily pad sometime in the future. For example, if we have three lily pads, the first one with fifty insects, the second one with thirty, and the third one with twenty, then over time the frog will be on the first pad 50 percent of the time, on the second one 30 percent of the time, and on the third one 20 percent of the time (see Figure 12.1).

图 12.1：三片睡莲，每片睡莲上的数字标签标明了不同数量的飞虫。我们假设在每个时间步骤中，青蛙都有同等的机会选择两片相邻的睡莲中的一片并根据 Metropolis 接受标准移到该睡莲上。左侧的图表说明了整体设计，标记的弧线提供了选择该邻居的概率（所有情况下均为 ½）× 接受概率。右侧顶部矩阵给出了所得马尔可夫链蒙特卡罗过程的转移概率，即假设您当前位于行指定的睡莲上，则移到列指定的睡莲上的概率。经过许多时间步骤后，系统收敛到底部转移矩阵，青蛙分别有 50%、30% 和 20% 的时间停留在有 50、30 和 20 只昆虫的睡莲上。这个底部矩阵是将顶部矩阵反复乘以自身的结果。

Figure 12.1: Three lily pads with different numbers of flying insects given by the numeric label in each pad. We assume that at each time step the frog has an equal chance of picking one of the two neighboring lily pads and moving to it based on the Metropolis acceptance criteria. The diagram on the left illustrates the overall design, with the labeled arcs providing the probability of choosing that neighbor (½ in all cases) × the acceptance probability. The top matrix on the right gives the transition probabilities for the resulting Markov chain Monte Carlo process, that is, the probability of moving to the pad designated by the column, given that you are currently on the pad designated by the row. After many time steps, the system converges to the bottom transition matrix, with the frog residing on the 50-, 30-, and 20-insect lily pads 50 percent, 30 percent, and 20 percent of the time, respectively. This bottom matrix is the result of repeatedly multiplying the top matrix by itself.

青蛙和池塘的规律同样适用于其他自适应系统。自适应系统中代理的配置代表系统的各种状态。代理通过以受限方式重新配置自身并转向可产生更好结果的新配置来追求目标。因此，如果我们愿意对现实进行一些关键的简化，我们可以生成复杂系统中自适应代理的有用模型，并使用 MCMC 思想推导出有关该系统行为的基本定理。

What’s true for frogs and ponds can also be true for other adaptive systems. Configurations of an agent in an adaptive system represent various states of the system. An agent pursues goals by reconfiguring itself in constrained ways and moving toward new configurations that result in better outcomes. So if we are willing to make some key simplifications of reality, we can generate a useful model of an adaptive agent in a complex system and use MCMC ideas to derive a fundamental theorem about this system’s behavior.

要开始这个过程，我们需要考虑代理如何表示各种状态。例如，在生物学中，生物体的基因型代表所有基因型系统的可能状态。在经济学中，状态可以表示公司的标准操作程序、产品设计、消费者的消费组合或某些行为规则。在城市中，状态可以表示道路网络或活动地点。

To begin this process, we need to think about how an agent represents various states. In biology, for example, an organism’s genotype represents a possible state of the system of all genotypes. In economics, states can represent, say, the standard operating procedures of a firm, the design of a product, the consumption bundle of a consumer, or some rule of behavior. In a city, states could represent the network of roads or the locations of activities.

给定自适应系统的状态空间，MCMC 方法需要使用提议分布识别新的可能状态的概念。对于表现良好的 MCMC，对提议分布形式的要求相对较低——只不过是最终从一个状态移动到另一个状态的合理能力。（为了方便，我们可能希望施加更多限制，例如要求此分布是对称的。）在自适应系统中，现有结构可以通过类似突变的运算符随机改变的概念往往是一个容易接受的假设，并且满足上述要求。事实上，突变是生物系统的核心，它也近似于在各种其他系统中观察到的行为。例如，新产品通常是旧产品的轻微变体，新技术或科学实体思想站在巨人的肩膀上，消费者对他们购买的商品做出微小的改变，等等。

Given the state space of an adaptive system, the MCMC approach requires a notion of identifying new possible states using a proposal distribution. For a well-behaved MCMC, the requirements for the form of the proposal distribution are relatively light—not much more than some reasonable ability to move, eventually, from one state to another. (For convenience, we might want to impose some more restrictions, such as requiring that this distribution be symmetric.) In adaptive systems, the notion that existing structures can be randomly altered by a mutation-like operator tends to be an easy assumption to embrace and one that meets the above requirements. Indeed, mutation is central to biological systems, and it also approximates the behavior observed in a variety of other systems. For example, new products are often slight variants of old ones, new technological or scientific ideas rest on the shoulders of giants, consumers make slight alterations in the goods that they buy, and so on.

对于系统的任何给定状态，算法都需要一个适应度度量。对于我们的青蛙来说，昆虫就是这个度量，因为青蛙吃的昆虫越多，它就越快乐。其他自适应系统中也出现了类似的适应度度量。例如，在生物学中，适应度的概念不仅与食物供应有关，还与生物体生存和繁殖的整体能力有关。在经济学中，我们经常认为代理人追求利润（就公司而言）或幸福（就消费者而言）。因此，只要自适应系统中的代理人追求目标，我们就可以使用该目标的度量作为驱动我们模型的手段。

The algorithm needs a measure of fitness for any given state of the system. For our frog, insects serve as this measure, as presumably the more insects the frog consumes, the happier it is. Similar measures of fitness arise in other adaptive systems. For example, in biology there is a notion of fitness that is tied not only to the food supply but also to the overall ability of an organism to survive and reproduce. In economics, we often think of agents pursuing profit (in the case of firms) or happiness (in the case of consumers). Thus, as long as agents in an adaptive system are pursuing a goal, we can use the measure of this goal as a means to drive our model.

最后，我们的模型要求自适应系统根据与 MCMC 兼容的接受标准采用所提出的变体。Metropolis 及其同事制定的标准 始终接受任何适应度高于现状的变体，当该变体的适应度低于现状时，标准会以概率方式采用该变体，随着两个选项之间的适应度差异增加，可能性会减小。对于许多自适应系统来说，这样的规则似乎是一种合理的近似值。

Finally, our model requires that the adaptive system adopt the proposed variant based on a MCMC-compatible acceptance criteria. The criteria developed by Metropolis and his coworkers always accepted any variant that had higher fitness than the status quo, and when the fitness of that variant was less than that of the status quo, the criteria adopted it probabilistically, with the likelihood diminishing as the difference in fitness between the two options increased. Such a rule seems to be a reasonable approximation for many adaptive systems.

可能还有其他验收标准也会导致详细平衡，从而提供所需的收敛。例如，如果提案分布是对称的，则采用具有变体的适应度除以变体和现状的适应度得出的概率也会产生详细平衡。 根据这样的规则，如果变体的值等于现状的值，则采用变体的概率为 50%，并且随着变体值的上升（下降），采用概率会增加（减少）远离 50%。 （顺便说一句，如果系统有验收标准但没有详细平衡，那么一切都不会丢失，因为它仍然会收敛到一个唯一的分布，但该分布将与下面指定的分布不同，尽管可能只是略有不同。）

There may be other acceptance criteria that will also result in detailed balance and thereby provide the needed convergence. For example, if the proposal distribution is symmetric, an acceptance criterion that adopts the variant with a probability given by the variant’s fitness divided by the fitness of both the variant and the status quo also results in detailed balance. Under such a rule, if the value of the variant is equal to that of the status quo, there is a 50 percent chance that it is adopted, and as the variant’s value rises (falls) the adoption probability increases (decreases) away from 50 percent. (By the way, all is not lost if the system has acceptance criteria without detailed balance, as it will still converge to a unique distribution, but that distribution will differ from the one specified below, though perhaps only slightly.)

假设我们有一个自适应系统，其中代理代表系统的可能状态。在每个时间步骤中，都会针对环境测试此代理的合理变体，并且该变体将根据与相对适应度相关的详细平衡兼容验收标准替换现有代理。这导致了复杂自适应系统的一个基本定理： 在上述自适应系统中，经过足够的磨合时间后，系统中代理（状态）的分布由标准化适应度分布给出。

Suppose we have an adaptive system where an agent represents a possible state of the system. At each time step, a reasonable variant of this agent is tested against the environment, and that variant replaces the existing agent based on detailed-balance-compatible acceptance criteria tied to relative fitness. This leads to a fundamental theorem of complex adaptive systems: in the above adaptive system, after sufficient burn-in time, the distribution of the agent (states) in the system is given by the normalized fitness distribution.

该定理的证明只是注意到上述系统正在实现 MCMC 算法，并且这种算法收敛到感兴趣的度量的（隐式）正则化分布 - 这里是接受标准中使用的适应度。

The proof of this theorem is simply noting that the above system is implementing a MCMC algorithm, and that such algorithms converge to the (implicitly) normalized distribution of the measure of interest—here, the fitness used in the acceptance criteria.

该定理意味着，一般来说，这种自适应系统会收敛到由标准化适应度控制的状态分布。因此，自适应代理并不是完美的能够找到并坚持解决它们所面临的问题的最佳方法。相反，它们倾向于集中精力于更好的解决方案（只要有足够的时间），尽管在极少数情况下它们会发现自己处于次优情况。如果我们把青蛙扔进池塘，让它有机会适应一段时间，当我们回来时，青蛙很可能在昆虫最多的荷叶上，但我们总有机会在其他荷叶上找到它——昆虫较少的荷叶上找到它的几率较低，但无论如何还是有机会的。

This theorem implies that, in general, such adaptive systems converge to a distribution of states governed by the normalized fitness. Thus, adaptive agents are not perfectly able to seek out, and remain on, the best solutions to the problems they face. Rather, they tend to concentrate on the better solutions (given sufficient time), though on rare occasions they will find themselves in suboptimal circumstances. If we throw our frog into the pond and give it a chance to adapt for a while, when we return the frog is most likely to be on the lily pad with the most insects, but there is always a chance that we will find it on any of the other lily pads—a lower chance for those lily pads with fewer insects, but a chance nonetheless.

该定理的一个含义是，虽然自适应代理往往表现良好，但它们并不完美。这种说法既令人欣慰又令人不安。虽然很高兴知道，如果有足够的时间，自适应系统往往会专注于世界上更适合的结果，但在极少数情况下，它们会最终导致糟糕的结果。虽然接受标准倾向于向空间中更好的部分移动，但系统总是有可能从高适应性结果转向低适应性结果。

One implication of the theorem is that while adaptive agents tend to do well, they are not perfect. Such a statement is both comforting and disconcerting. While it is nice to know that, given sufficient time, adaptive systems tend to concentrate on the fitter outcomes in the world, on rarer occasions they will end up in the bad outcomes. While the acceptance criteria tend to bias movement toward better parts of the space, there is always a chance that the system will move from a high-fitness outcome to a low-fitness one.

这里显而易见的问题是，通过避免这种降低适应度的举动，系统是否会变得更好。通过防止这样的举动，我们可以确保算法总是走向适应度更高的区域，但正如我们在第 5 章中看到的那样，这样的算法很容易陷入局部最大值——即所有道路都通向下坡的点，即使远处有更高的地形。因此，需要接受较低的适应度是必要之恶，可防止系统陷入局部最大值。

The obvious question here is whether the system would be better off by avoiding such fitness-decreasing moves. By preventing such moves, we could ensure that the algorithm always walks toward areas of higher fitness but, as we saw in Chapter 5, such an algorithm can easily get caught at a local maximum—a point where all roads lead downhill even though much higher terrain exists in the distance. Thus, the need to accept configurations of lower fitness is a necessary evil that prevents the system from getting stuck on local maxima.

可以通过引入温度来修改算法，就像在模拟退火中所做的那样。在过程的早期，温度保持较高，使算法能够正常进行。随着时间的推移，我们冷却搜索，减少接受降低适应度的移动的机会。如果有足够的时间和精心控制的退火计划，系统将倾向于锁定在适应度较高的区域。但这种退火计划的设计很棘手，一旦系统冷却下来，它就无法适应底层适应度景观的变化。

One could modify the algorithm by, say, introducing a temperature, as is done in simulated annealing. Early on in the process, the temperature is kept high, allowing the algorithm to proceed normally. As time passes, we cool the search, lessening the chance of accepting fitness-reducing moves. Given enough time and a carefully controlled annealing schedule, the system will tend to lock into areas of higher fitness. But the design of such annealing schedules is tricky, and once the system is cooled, it would be unable to adapt to a change in the underlying fitness landscape.

请注意，该定理要求足够的磨合时间。回想一下，马尔可夫链将下一个状态的概率与当前状态联系起来。从这个意义上说，它们有一定的记忆力，因为你现在的位置会影响你在短期内可以去的地方。在适当的条件下（在我们的定理中成立），这些初始影响会随着时间的推移而消失，链中的后续环节由表征马尔可夫过程的更基本的力量驱动。磨合是系统忘记其初始条件并落入其基本分布所需的时间。所需的磨合时间取决于许多因素。随着我们增加底层空间的大小，磨合时间也会增加，因为探索更大的空间需要更长的时间。此外，磨合时间可能会受到我们的提议分布的影响。如果如果提议分布产生的变体非常接近现状，那么马尔可夫链的形成速度就会很慢，因为搜索过程非常缓慢。相反，如果变体远离现状，那么很可能会被拒绝，链的速度也会再次变慢。最后，空间本身的形状会影响磨合时间。例如，如果存在大片适应度较低的区域，那么链可能会在这些荒凉的平原上停留很长时间，然后才会出现在空间中适应度较高的部分。

Note that the theorem requires sufficient burn-in time. Recall that Markov chains link the probability of the next state to the current state. In this sense they have some memory, since where you are now influences where you can go in the short run. Under the right conditions (which hold in our theorem), these initial influences dissolve away over time and the subsequent links in the chain are driven by the more fundamental forces characterizing the Markov process. Burn-in is the amount of time it takes for the system to forget its initial conditions and fall into its fundamental distribution. The needed burn-in time depends on a number of factors. As we increase the size of the underlying space, the burn-in time increases, since it takes longer to explore the larger space. Moreover, the burn-in time can be influenced by our proposal distribution. If the proposal distribution produces variants that are very close to the ­status quo, then the Markov chain will be slow to form, given the plodding search. If instead the variants are far from the status quo, then rejections are quite likely, and again the chain will slow down. Finally, the shape of the space itself can influence burn-in time. For example, if there are large areas of low fitness, the chain can get caught in these desolate flatlands for long periods of time before it happens upon the fitter parts of the space.

不幸的是，除了上述直观论据之外，我们在理论层面上简洁地描述老化过程的能力非常有限。尽管如此，老化对自适应系统还是有一些有趣的含义。虽然我们的定理保证自适应系统最终会落入正则化适应度分布，但这种情况发生的速度取决于它穿越老化期的速度。具有更大状态空间、更多异常适应度景观、特别糟糕的起始条件或生成太近或太远变体的提议分布的系统往往会妨碍自适应快速收敛到由正则化适应度分布控制的更适应变体的能力。从这个意义上说，较长的老化时间使自适应更加困难。

Unfortunately, other than the intuitive arguments above, our ability to succinctly characterize the burn-in process at a theoretical level is quite limited. Nonetheless, burn-in has some interesting implications for adaptive systems. While our theorem guarantees that the adaptive system will eventually fall into the normalized fitness distribution, the speed at which this happens depends on how quickly it can traverse the burn-in period. Systems with larger state spaces, more anomalous fitness landscapes, particularly bad starting conditions, or proposal distributions generating variants that are either too near or too far will tend to hamper the ability of adaptation to quickly converge on the fitter variants governed by the normalized fitness distribution. In this sense, longer burn-in times make adaptation more difficult.

上述定理与所有定理一样，都是基于一组简化。它假设自适应系统通过从一个结构行进到下一个结构来工作，并通过提议分布生成新的结构并根据与所提议变体的相对适应度相关的接受标准而被接受。这是一个有点静态的模型，因为适应度分布是不变的，因为相同的结构永远获得相同的适应度测量。在更现实的系统中，人们可能希望包含一个内生的适应度概念，即给定结构的适应度取决于世界上还有哪些其他结构。这可能通过在模型中扩展结构概念来实现。它不是将其视为定义单个代理，而是可以定义整个代理群体，但这种阐述并不简单，因为适应度函数通常是在个体层面而不是群体层面定义的。在这样一个扩展的系统中，就好像我们正在运行多个 MCMC 算法，每个代理都适应由其他结构创建的（瞬态）世界。

The above theorem, like all theorems, was predicated on a set of simplifications. It assumes that adaptive systems work by marching from one structure to the next, with new structures being generated via a proposal distribution and being accepted based on acceptance criteria that are tied to the relative fitness of the proposed variant. This is a somewhat static model, as the fitness distribution is unchanging in the sense that the identical structure gets the same measure of fitness in perpetuity. In more realistic systems, one might want to include an endogenous notion of fitness, whereby the fitness of a given structure depends on, say, what other structures are in the world. This may be possible by extending the notion of structure in the model. Instead of thinking of it as defining a single agent, it could define an entire population of agents, but such an elaboration is non-trivial, since the fitness function is typically defined at the level of the individual, not at the group level. In such an extended system, it is as if we are running multiple MCMC algorithms, with each agent adapting to the (transient) world created by the other structures.

推动我们定理的另外两个关键要素是提议分布和接受标准。如果提议分布的选择合理，MCMC 算法往往相当稳健，但如上所述，这种选择可能会影响磨合时间。不幸的是，除了调整搜索距离会影响磨合时间这一概念外，很难得出关于提议分布和磨合时间之间关系的清晰理论结果，其中跳跃范围既不太大也不太小，导致磨合时间最快。

The other two key elements driving our theorem are the proposal distribution and the acceptance criteria. MCMC algorithms tend to be fairly robust if the choice of the proposal distribution is reasonable, though, as noted, this choice may influence burn-in time. Unfortunately, clean theoretical results about the relationship between proposal distributions and burn-in time are difficult to derive, apart from the notion that tuning the distance of the search can influence burn-in time, with a Goldilocks-like region of jumps that are neither too large nor too small leading to the fastest burn-in time.

接受标准是算法的另一个有趣元素。Metropolis 算法中使用的原始接受标准是由设计的必要性驱动的，虽然它们为许多自适应过程提供了合理的模拟，但其他标准可能也很有趣。有替代的接受函数，例如，一些使用更直接的相对适应度测量的函数也可以产生详细的平衡，从而允许系统按照定理收敛。更好地描述导致详细平衡的接受标准类别将很有用。此外，即使详细平衡不成立，系统仍然会收敛到一个唯一的状态分布，但该分布不会由标准化适应度给出。在这些情况下，替代的接受标准仍有可能导致系统行为接近上述结果，或者具有其自身的有趣含义。

The acceptance criteria are another interesting element of the algorithm. The original acceptance criteria used in the Metropolis algorithm were driven by necessity of design, and while they provide a reasonable analog to a lot of adaptive processes, other criteria may be of interest. There are alternative acceptance functions, for example, some that use a more direct measure of relative fitness that can also result in detailed balance, thereby allowing the system to converge as per the theorem. Having a better characterization of the class of acceptance criteria that results in detailed balance would be useful. Also, even when detailed balance doesn’t hold, the system still converges to a unique state distribution, but that distribution will not be given by the normalized fitness. In these cases it is still likely that the alternative acceptance criteria will lead to system behavior that approximates the results above or, alternatively, have interesting implications of their own.

本章以战争的迫切需要为开篇，战争的迫切需要让我们了解相互作用的原子系统，并开发出新的工具（如可编程计算机）和方法（如蒙特卡罗），以便为此类系统提供必要的见解。故事发生在原子时代和信息时代的黎明，是一个充满天才的故事，有时甚至充满趣味。我们复杂的三位一体是通过重新利用战争算法来获得一些关于复杂系统中自适应代理行为的基本见解而完成的。我们发现，这些代理在不知不觉中实施了一种算法，这种算法将它们锁定在宇宙的适应舞蹈中。正如大都会所指出的，“可惜的是，战争似乎是启动这种革命性科学努力的必要条件。”

We began this chapter with the exigencies of war, which resulted in the need to understand interacting atomic systems and to develop novel tools (such as programmable computers) and methods (such as Monte Carlo) that could be used to provide essential insights into such systems. Taking place at the dawn of both the atomic and information ages, it is a story of great genius and, at times, even playfulness. Our complex trinity was completed by repurposing the algorithms of war to gain some fundamental insights into the behavior of an adaptive agent in a complex system. We find that such agents are unknowingly implementing an algorithm that locks them into a cosmic dance of fitness. As Metropolis noted, “What a pity that war seems necessary to launch such revolutionary scientific endeavors.”

a 看来，恩里科·费米在 20 世纪 30 年代早期曾使用类似蒙特卡罗的方法来解决中子扩散问题。显然，他喜欢通过失眠期间进行的秘密机械计算来提供相当准确的实验结果预测，从而给同事留下深刻印象。早期也有使用随机性进行重要计算的例子，例如 18 世纪的布丰针被用来近似 π 的值。

a It appears that Enrico Fermi used Monte Carlo–like methods in the early thirties to solve problems in neutron diffusion. Apparently he enjoyed impressing his colleagues by offering quite accurate predictions of experimental outcomes based on clandestine mechanical calculations made during bouts of insomnia. There are also earlier examples of using randomness to perform important calculations, such as Buffon’s needle from the eighteenth century being used to approximate the value of π.

b 所有正则链都是遍历链，但并非所有遍历链都是正则链。例如，如果你有一个双态系统，在每个时间步长上从一个状态切换到另一个状态，那么它将是遍历链，因为它可以从任何状态切换到任何其他状态，但不是正则链，因为它仅在偶数或奇数时间步长上访问给定状态。

b All regular chains are ergotic, but not all ergotic chains are regular. For example, if you have a two-state system that alternates from one state to the other at each time step, it will be ergotic, because it is possible to go from any state to any other state, but not regular, since it visits a given state only on either even or odd time steps.

结语：博学的天文学家

Epilogue: The Learn’d Astronomer

当我听到那位博学的天文学家

When I heard the learn’d astronomer,

当那些证明和数字在我面前一一排列时，

When the proofs, the figures, were ranged in columns before me,

当我看到这些图表和图解，并要我添加、划分和测量它们时，

When I was shown the charts and the diagrams, to add, divide, and measure them,

当我坐在教室里听天文学家演讲，并赢得热烈掌声时，

When I sitting heard the astronomer where he lectured with much applause in the lecture-room,

我很快就不知不觉地感到疲倦和不适，

How soon unaccountable I became tired and sick,

直到我站起身，独自走开，

Till rising and gliding out I wander’d off by myself,

在神秘潮湿的夜空中，时不时地，

In the mystical moist night-air, and from time to time,

静静地仰望星空。

Look’d up in perfect silence at the stars.

—沃尔特·惠特曼， 《草叶集》

—Walt Whitman, Leaves of Grass

西我们都曾以某种形式听过博学天文学家的言论。也就是说，我们遇到了精心设计的分析，虽然可能值得称赞，但似乎与我们想要凝视和了解的星星完全脱节。

We have all heard the learn’d astronomer in one form or another. That is, we have encountered a carefully laid out analysis that, while perhaps worthy of applause, seems terribly disconnected from the stars we wish to gaze upon and know.

现代学术界普遍存在类似的不安。我们仔细分析了大脑中的化学反应或简化拍卖中的最佳竞标策略，但这些研究与真正令我们惊叹的现象（如大脑思考的能力或市场组织交易的能力）之间的联系似乎相当似是而非。

A similar discomfort is pervasive in modern academics. We have carefully worked out analyses of, say, the chemical interactions in the brain or the optimal bidding strategy in a simplified auction, yet the connection from these studies to the phenomena that truly awe us, such as the ability of brains to think or markets to organize trades, seems rather specious.

虽然我们可能想责怪科学家们关心错误的事情，但这并不容易。还原论的世界观——将复杂的事物分解成其组成部分，然后仔细分析这些部分，直到我们了解它们——提供了一个有用的阿基米德支撑点，让我们可以理解复杂的世界。不幸的是，我们只能用这些工具来推动世界的发展。

While we might want to blame the scientists for caring about the wrong things, it’s not that easy. The reductionist approach to the world—breaking down complicated things to their constituent parts and then carefully dissecting these parts until we know them—has provided a useful Archimedean purchase from which to lever our complex world into the light of understanding. Unfortunately, there is only so far we can move the world using such tools.

正如我们在本书中看到的，了解部分并不等于了解整体。简化并不能告诉我们构造。这是复杂系统研究的基本见解。即使我们能够完全理解单个工蜂、市场交易员或神经元的行为如何由其环境决定，我们也几乎不知道蜂巢、市场或大脑的运作方式。要真正理解蜂巢、市场和大脑，我们需要了解蜜蜂、交易者和神经元之间的相互作用如何导致整个系统的总体行为。以一只工蜂为例，全面分析她对所接收的化学、视觉和听觉输入的反应，我们就能获得一些关于简单生物如何对其世界做出反应的新知识。以一群这样的蜜蜂为例，让它们互动，我们开始看到新的行为出现，这些行为虽然显然与每只蜜蜂的行为有关，但同时又与这些行为完全无关，而且很难仅从我们对单个工蜂的观察中预测出来。与我们所知的其他生物（包括我们自己）一样，这个新出现的实体能够调节自己的体温、收集所需的营养物质、储存和使用能量、保护自己免受外界侵害、处理废物、攻击内部和外部威胁，甚至繁殖。

As we have seen throughout this book, knowing the parts is not equivalent to knowing the whole. Reduction does not tell us about construction. This is the fundamental insight of the study of complex systems. Even if we could fully understand how an individual worker bee’s, market trader’s, or neuron’s behavior is determined by its environment, we would have little idea about how a hive, market, or brain works. To truly understand hives, markets, and brains, we need to understand how the interactions of honeybees, traders, and neurons result in system-wide, aggregate behavior. Take a single worker bee and fully analyze how she responds to the chemical, visual, and audio inputs she receives, and we gain some new knowledge about how a simple organism responds to its world. Take a hive of such honeybees and allow them to interact, and we begin to see new behaviors emerge that, while obviously tied to the actions of each individual honeybee, are at the same time wholly disconnected from these actions and not easily predicted from only our observations of the individual worker. Like other biological organisms that we know (including us), this newly emerged entity has the ability to regulate its own temperature, gather needed nutrients, store and use energy, protect itself from outsiders, dispose of waste, attack internal and external threats, and even reproduce.

复杂系统科学的终极希望是，蜜蜂蜂巢、金融市场和大脑之间有着深厚的联系，或者说，它们与其他生物有机体、城市、公司、政治系统、计算机网络等并没有什么不同。蜜蜂群可能只是大脑的一个更容易观察的实例。如果是这样，那么做出更好选择的正反馈和基于群体的触发以最终做出决定的一般过程可能不仅会驱动蜂群的选择，还会驱动我们自己的选择。

The ultimate hope in the science of complex systems is that honeybee hives, financial markets, and brains are deeply connected—or, for that matter, not all that different from other biological organisms, cities, companies, political systems, computer networks, and on and on. A honeybee swarm may just be a more easily observed instance of a brain. If so, the general processes of positive feedback for better choices and quorum-based triggers to finalize the decision may drive not only a swarm’s choices but also our own.

在过去的二十年里，各种复杂系统思维逐渐汇聚成一幅新兴的理解挂毯，它考虑的不只是某一个特定事物，而是整体。这幅挂毯的经线在科学的织机上紧紧拉紧，由复杂系统研究中不可或缺的关键思想和工具组成。纬线穿过经线并将其连接在一起，开始填充一个慢慢出现的图案。许多编织者都在制作这幅挂毯，每个人都试图在自己的作品中保持连贯性和美感。最近，我们开始看到这些不同的部分开始相互融合，只留下淡淡的懒散线条，就像纳瓦霍地毯上看到的线条一样。这里探讨的各种复杂系统思想和例子开始创造出一幅美丽而实用的挂毯。

Over the last two decades, various strands of complex-­systems thinking have slowly come together in an emerging tapestry of understanding that considers not just one particular thing but the whole. The warp of this tapestry, stretched tight on the loom of science, is composed of the key ideas and tools that have become integral to the study of complex systems. The weft, weaving through the warp and binding it together, is beginning to fill in a slowly emerging pattern. There are many weavers working on this tapestry, each attempting to keep coherence and beauty in her own part of the work. Recently we have been starting to see these various pieces begin to meld into one another, marked only by faint lazy lines like those seen in Navajo rugs. The various strands of complex-systems ideas and examples explored here are starting to create a beautiful, and quite useful, tapestry.

我们开始探索复杂系统，观察简单的局部行为一旦连接起来，如何产生新的全球模式。这类系统在我们的世界中比比皆是，我们现在知道，从简单的开始，我们可以得到奇妙的结果。小片彩色玻璃一旦连接起来，就会形成一扇彩色玻璃窗，在我们的心目中创造出一幅图像，激发我们的信仰和灵性。即使现在，当你读到这些文字时，像素正在变成字母，字母正在变成单词，单词正在发展意义，意义正在融入思想。

We began our exploration into complex systems by looking at how simple, local actions, once connected, can result in new global patterns. These types of systems abound in our world, and we now know that from simple beginnings we can get marvelous ends. Small pieces of colored glass, once connected, result in a stained-glass window that creates an image in our mind’s eye that inspires faith and spirituality. Even now, as you read these words, pixels are becoming letters, letters are becoming words, words are developing meaning, and meaning is rolling into thought.

为了理解简单的部分如何产生全局模式，我们使用了细胞自动机的数学原理。这些抽象的创造物与计算机的实用性相结合，有助于将其含义可视化，展示了简单、局部、分散的过程如何产生全局模式。

To understand how simple parts result in global patterns, we used the mathematics of cellular automata. These abstract creations, linked with the utility of a computer to help visualize their implications, show how simple, local, decentralized processes can result in global patterns.

两百多年前，亚当·斯密曾援引“看不见的手”——与“奇迹发生”相差无几——来解释交易者的个人行为如何导致并非任何人本意的结果，这些行为都是为了自己的利益。当我们研究熙熙攘攘的集市中发生的交易时，复杂系统视角开始显现出斯密的指导之手。当条件合适时，市场会利用简单开端的力量，形成新兴的全球模式（价格），以最佳方式分配资源和经济生产。

More than two hundred years ago, Adam Smith invoked the “invisible hand”—not far removed from “then a miracle happens”—to explain how the individual actions of traders, each out for her own gain, result in an outcome that was no part of anyone’s intention. The complex-­systems perspective begins to make visible Smith’s guiding hand as we investigate the trades that arise in a bustling bazaar. Markets, when conditions are right, leverage the power of simple beginnings to lead to emerging global patterns (prices) that allocate resources and economic production to best use.

当系统简单时，我们可以轻松地跟踪其行为的每个步骤，从而准确预测整个系统的行为。当系统复杂时，这种跟踪就变得困难得多，因为每次新的跟踪都会改变之前的跟踪，这使得跟踪变得极其棘手，有时甚至无法预测会发生什么——例如，2010 年 5 月 6 日，堪萨斯州肖尼传教团的一台计算机在其交易程序中犯了一个看似微不足道的错误，并产生了一个意料之外的反馈循环，给金融界带来了严重破坏。

When systems are simple, we can easily trace their behavior from step to step, and in so doing make accurate predictions about the overall system’s behavior. When systems are complex, such tracing becomes far more difficult, as each new trace alters previous ones, making it extremely tricky and at times impossible to predict what will happen—as when, on May 6, 2010, a computer in Shawnee Mission, Kansas, compounded a seemingly insignificant error in its trading program and created an unanticipated feedback loop that wreaked havoc on the financial shores.

每当我们连接系统时，我们都会建立反馈回路。某些类型的反馈会产生稳定的力量，使整个系统平静下来。可惜的是，其他类型的反馈会破坏系统的稳定性，即使经过仔细思考和设计，也很容易构建出带有无意的（和不幸的）反馈回路的系统。2008 年全球金融危机的影响至今仍在上演，这是由于系统中的每个部分似乎都是合理的（或者至少对局部激励做出了合理的反应）。不幸的是，对部分而言正确的并不适用于整体，而各部分之间的相互联系导致了一系列反馈回路，能够摧毁全球经济。我们经常听说一些灾难性事件是“完美风暴”事件的结果。然而，在一个日益复杂的世界中，我们只是在完善我们创造这种风暴的能力。

Anytime we interconnect systems, we build in feedback loops. Some types of feedback result in stabilizing forces, calming the system as a whole. Alas, other types of feedback destabilize systems, and even with careful thinking and design, it is easy to build systems with unintentional—and unfortunate—feedback loops. The worldwide financial collapse of 2008, the reverberations of which are still playing out today, was the result of a system in which each of the parts seemed rational—or at least responded in a reasonable way to local incentives. Unfortunately, what was true for the parts was not true for the whole, and the interconnections among the parts resulted in a series of feedback loops able to take down a worldwide economy. We often hear that some disastrous event was the result of a “perfect storm” of events. However, in a world of increasing complexity, we are simply perfecting our ability to create such storms.

当复杂性大量存在时，多样性就显得至关重要。由同质代理组成的系统与由异质代理组成的系统的行为截然不同。同质系统的所有代理都会根据相同的线索采取相同的行动，因此对新事件的反应可能比异质系统更加激烈。因此，如果我们想更好地预测系统的行为，我们需要明确考虑其异质性，而不是依赖代表性（因此也是同质的）代理等理论上的权宜之计。

When complexity abounds, diversity matters. Systems composed of homogeneous agents behave quite differently than those composed of heterogeneous ones. Homogeneous systems, with all of the agents taking the same actions based on the same cues, can have much more dramatic responses to new events than heterogeneous ones. Thus, if we want to predict better how a system will behave, we need to account explicitly for its heterogeneity rather than rely on theoretical expediencies such as representative (and hence homogeneous) agents.

异质性的价值取决于我们正在考虑的系统。当需要渐进式响应时，异质性很有用，因此在蜜蜂试图控制蜂巢温度或交易者等系统中想要稳定价格，异质性越多越好。然而，在其他系统中，这种异质性是有害的。政府想要控制社会运动，细菌群体想要释放毒素，异质性越少越好。

The value of heterogeneity depends on the system we are considering. Heterogeneity is useful when a graduated response is needed, and so in systems like honeybees attempting to control their hive’s temperature or traders wanting to stabilize prices, having more heterogeneity is better. However, there are other systems where such heterogeneity is detrimental. A government wanting to control a social movement or a population of bacteria wanting to release a toxin might benefit from less heterogeneity.

当复杂性泛滥时，寻找问题的解决方案通常很困难。复杂系统中固有的各种相互依赖性和反馈使得在此类系统中寻找新解决方案变得极其困难。在我们这个世界不太复杂的部分，寻找好的答案就像攀登富士山，只要你一直往上走，你就会到达山顶。在这样的世界里，错误——朝错误的方向迈出一步——只会阻碍进步。复杂系统涉及一种非常不同的搜索，其中的山脉不仅崎岖不平，而且雾气弥漫，甚至可能随着我们的每一步而起伏不定。当我们由相互关联和相互依赖的部分组成整体时，这种复杂的山脉很常见，例如我们在消费品、技术、制造工艺和药物鸡尾酒中看到的那样。在这样的世界里，即使我们毫无差错地爬上雾气弥漫的山峰，我们也可能会错过风景的最高点。事实上，我们可能会发现自己胜利地站在一个小土丘上，错误地认为我们已经到达了山顶。为了避免小题大做，我们需要在复杂的世界中寻找新方法。特别是，在我们的搜索过程中引入错误——即偶尔采取随意走下山的脚步——也许能让我们逃离小土丘的陷阱，走向山顶。

When complexity abounds, discovering solutions to problems is often difficult. The various interdependencies and feedbacks that are innate in a complex system make searching such systems for new solutions extremely hard. In less complex parts of our world, finding good answers is like climbing Mount Fuji, where if you just keep going uphill, you will reach the top. In such a world, errors—taking a step in the wrong direction—only hamper progress. Complex systems involve a very different kind of search, where the mountain range is not only rugged but also fog-bound, and perhaps even undulating with every step we take. Such complex ranges are common when we have interconnected and interdependent pieces making up the whole, such as we might see in consumer goods, technologies, manufacturing processes, and drug cocktails. In such a world, even if we hike up the fog-bound hill without error, we might miss the highest point on the landscape. Indeed, we might find ourselves victoriously standing on top of a molehill, falsely thinking that we have made it to the top of the mountain. To avoid making mountains out of molehills, we need new ways to search in complex worlds. In particular, introducing errors into our search process—that is, occasionally taking random steps downhill—may allow us to escape the trap of the molehill and head to the mountaintop.

当复杂性泛滥时，决策就会变得无处不在。作为有思想的生物，我们很容易相信决策需要智慧，智慧需要大脑。然而，在一个充满复杂联系和互动的世界里，简单的部分可以产生明智的决策。

When complexity abounds, decision making becomes ubiquitous. As thinking beings, we find it all too easy to believe that decision making requires intelligence, and that intelligence requires a brain. Yet in a world of complex connections and interactions, simple parts can result in intelligent decisions.

从我们免疫系统中的白细胞到我们体内栖息的大量细菌，每秒都在做出数以万亿计的智能决策，而不需要任何神经元。我们生活在计算和决策的海洋中。大自然通过将简单的化学和物理过程联系在一起，创造了能够从世界获取输入、记住输入并以有用的方式对其采取行动的生物计算机。

From the white blood cells in our immune systems to the multitude of bacteria inhabiting our bodies, trillions upon trillions of intelligent decisions are being made every second, without a neuron to be had. We live in a sea of computation and decision making. Nature has, by linking together simple chemical and physical processes, created biological computers capable of taking input from the world, remembering it, and acting upon it in useful ways.

这种生物决策系统是由进化形成的，无需由神经元驱动的大脑即可运行，能够做出明智的选择。令人惊讶的是，即使是低等的细菌也会根据明确的偏好采取行动。更令人惊讶的是，就像大脑发达的人类兄弟一样，这些简单的系统也会受到决策过程中各种偏见的影响，导致表现不佳。神经元很有用，因为它们可以快速地将信号传递到（生物学上的）很远的距离，但当然许多生物并没有那么大。一旦我们不再需要神经元，所使用的决策过程细菌和人类的思维方式可能并没有什么不同。我们可能生活在一个思维无处不在的世界。

Such biological decision-making systems, shaped by evolution and operating without a neuron-driven brain, are capable of making intelligent choices. Remarkably, even lowly bacteria are taking actions driven by well-defined sets of preferences. More surprising is that, like their big-brained human brethren, these simple systems also fall prey to various biases in decision making that result in suboptimal performance. Neurons are useful in that they can quickly transmit signals across (biologically) large distances, but of course many organisms are not all that big. Once we give up the need for neurons, the decision-making processes used by a bacterium and a human may not be all that different. We may well exist in a world where thinking is everywhere.

如果个体决策和智能不需要大脑的存在，那么思考这种智能如何出现在代理集合中就不难了。例如，蜜蜂工蜂具有一组有限的行为，这些行为与清洁蜂巢、哺育幼虫、形成蜂巢、采集花蜜和花粉等有关。但是，如果将数千只这样的工蜂放入一个蜂群中，我们就会得到一组全新的、有用的、蜂群级别的行为。在数千只蜜蜂的相互作用中，出现了一个能够进行生存测试的行为组合的超有机体。蜜蜂集合的正确性也适用于其他类型代理的集合。每年，有数以万计的录制歌曲被发行，社会试图通过十大榜单等来识别出最好的歌曲。我们从蜂群中得到的见解很容易应用到Billboard Hot 100 榜单上，因为一首特定歌曲进入榜单的可能性与其质量和被收听的频率间接相关。政治初选和公众辩论也受类似机制的影响。

If individual decision making and intelligence do not require the existence of a brain, then it is not too far a leap to think about how such intelligence could emerge in collections of agents. For example, a honeybee worker has a limited set of behaviors tied to cleaning the hive, nursing brood, forming comb, collecting nectar and pollen, and so on. However, place thousands of such workers into a colony, and we get an entirely new set of useful, colony-level behaviors. Out of the interactions of thousands of honeybees emerges a superorganism capable of a survival-tested behavioral repertoire. And what is true for a collection of honeybees also holds for collections of other types of agents. Each year, tens of thousands of recorded songs are released, and society attempts to identify the better ones via top-ten lists and the like. It is not hard to take the insights we gained from swarming honeybees and apply them to the Billboard Hot 100 list, as the likelihood of a particular song making it onto the list is indirectly tied to its quality and to how often it gets heard. Political primaries and public debates are subject to similar mechanisms.

群体决策最有趣的关联之一就是我们自己的意识。大脑中的神经元和蜂群中的蜜蜂可能并没有什么不同，如果是这样，我们就有了一种思考思维的新方式。沿着这样的路径走下去，蜜蜂身上出现的蜂群思维可能解释了我们自己的蜂群思维。

One of the most intriguing links to group decision making is to our own consciousness. Neurons in the brain and honeybees in a colony may not be all that different, and if so, we have a new way to think about thinking. Following such a path suggests that the mind of the hive that emerges in honeybees may explain the hive of our own mind.

当复杂性大量存在时，连接网络就变得至关重要。这些网络决定了代理的交互可能性，从而导致全局模式的出现。有时这些模式很有用，例如成群的蜜蜂为下一个蜂巢找到一个好位置。其他时候，网络会导致不良结果。例如，即使我们一开始只是与那些稍微喜欢与同类人生活在一起的人生活在一起，我们也很容易最终形成一个高度隔离的社会。对社区适用的规则也适用于政治选择、宗教信仰、犯罪和其他社会规范。我们生活在这样一个世界，随着复杂性在网络上发挥作用，即使是良好的意图也很容易被压垮，迫使我们走向一个没有人打算或想要的结果。

When complexity abounds, networks of connections matter. These networks, determining the interaction possibilities of agents, result in the emergence of global patterns. Sometimes these patterns are useful, as in the case of swarming honeybees finding a good location for the next hive. Other times, networks result in undesirable outcomes. For example, even if we begin with people who have only a slight preference to live among similar types of people, we can easily end up with a highly segregated society. What is true for a neighborhood is also true for political choices, religious beliefs, crime, and other social norms. We live in a world where even good intentions can easily get overwhelmed as complexity plays out over the network, forcing us to an outcome that no one intended or desired.

当复杂性大量存在时，缩放定律可能占上风。我们只是在慢慢地发现可能支配我们所居住的各种复杂系统的潜在定律。知道一个国家最大城市的人口，我们就可以知道第二大城市的人口。知道老鼠的心率，我们可以知道大象的寿命。知道一千人死亡的战争次数，我们可以知道一百万人死亡的战争次数。

When complexity abounds, scaling laws may prevail. We are only slowly uncovering the potential laws that may govern the various complex systems we inhabit. Knowing the population of the largest city in a country can tell us the population of the second-largest city. Knowing the heart rate of a mouse can tell us the life span of an elephant. Knowing the number of wars in which a thousand people died can tell us the number of wars in which a million will perish.

缩放定律的存在不仅在经验上很方便，而且在理论上也表明了系统之间更深层次的统一。我们推导生物系统缩放定律的方法也可能有效对于社会和人工系统也是如此。城市是需要运输、储存和使用能量的有机体，因此城市可能表现出类似于生物系统的缩放定律。过去一个世纪的主要人口趋势是人口持续增长和城市化进程加快。我们现在生活在一个拥有 70 多亿人口的世界里，其中一半以上生活在城市地区。了解城市的幂律将为我们在这个星球上的未来前景提供关键的见解。

The existence of scaling laws is not only empirically convenient but also theoretically suggestive of a deeper unification among systems. The same approach that allows us to derive scaling laws for biological systems may also work for social and artificial systems as well. Cities are organisms that require energy to be transported, stored, and used, and thus cities might exhibit scaling laws akin to biological systems. The key demographic trends over the last century have been continued population growth and increased urbanization. We now exist in a world of more than 7 billion people, with more than half of them living in urban areas. Knowing the power laws of cities will give us key insights into our future prospects on this planet.

当复杂性大量存在时，合作就会出现。合作能力是我们人类成功的关键因素。在大多数社会世界中，竞争会让你略微好过一点，而合作会让你好过很多。不幸的是，个人激励往往倾向于竞争而不是合作。

When complexity abounds, cooperation can emerge. The ability to cooperate is a key element in the success of our species. In most social worlds, competition makes you slightly better off, while cooperation makes you remarkably better off. Unfortunately, individual incentives tend to favor competition over cooperation.

尽管个人激励机制预测世界将变得血腥残暴，但复杂系统中出现的合作案例足以给我们带来一线希望。巴厘岛的水稻种植条件似乎有利于次优的竞争结果。然而，随着人类和自然生态系统的联系越来越紧密，农民开始合作和协调他们的农业活动，从而为所有人提供了更多的粮食。

Notwithstanding a world red in tooth and claw predicted by individual incentives, there are enough examples of cooperation emerging in complex systems to provide a ray of hope. Rice farming on the island of Bali occurs ­under conditions that seemingly favor the suboptimal, competitive outcome. Yet as the human and natural ecosystems became more tightly coupled, farmers began to cooperate and coordinate their farming activities, resulting in more food for all.

尽管竞争似乎有充分的理由占上风，但其他系统中似乎也出现了合作。使用进化的抽象模型计算机程序，我们可以探索合作的起源。在这样的世界中，当不断发展的策略重新利用其早期的游戏玩法并学会相互交流并发出合作意愿时，合作就会出现。当发出并采取行动时，类似秘密握手之类的东西就会自发出现，作为一种区分自己和他人的方式，合作就可以蓬勃发展。

Cooperation appears to emerge in other systems as well, despite what appear to be compelling reasons for competition to prevail. Using abstract models of evolving computer programs, we can explore the origins of cooperation. In such worlds, cooperation emerges when evolving strategies repurpose their early plays of the game and learn to communicate with one another and signal a willingness to cooperate. When such signals are sent and acted upon, something like a secret handshake spontaneously arises as a way to distinguish self from other, and cooperation can thrive.

当复杂性大量存在时，自组织临界性就会出现。复杂系统通常会自我组织成体现无意识秩序的特征配置。这种秩序意味着系统处于行动的边缘。自组织临界系统会创造一个活动可以发生在所有规模上的世界。大多数事件往往会导致小规模的局部雪崩，但很少会出现小事件导致整个雪崩的情况。

When complexity abounds, self-organized criticality can arise. Complex systems often organize themselves into characteristic configurations that embody unintentional order. This order implies a system that is near the edge of action. Self-organizing critical systems result in a world where activity can occur across all scales. The majority of events tend to result in small, localized avalanches, though rarely a small event can result in an avalanche that encompasses the entire pile.

某些类型的社会系统也可能自组织进入临界状态。在这些系统中，通常不会产生太大影响的小动作（例如偏远城镇中绝望的突尼斯街头小贩的抗议）有时会引发重大后果，例如 2010 年底开始的中东地区政府推翻浪潮，即所谓的“阿拉伯之春”。

Certain types of social systems may self-organize into critical states as well. In these systems, small actions that normally have little consequence, such as the protest of a desperate Tunisian street vendor in a remote town, can at times trigger large results, such as the subsequent wave of government overthrows across the Middle East starting in late 2010, known as the Arab Spring.

在我们试图理解复杂性的过程中，复杂性无处不在。利用原子进行战争的愿望催生了一个由相互作用的人、思想和技术组成的非凡网络。从这个网络中诞生了一项普罗米修斯式的交易，不仅创造了人类有史以来最具破坏性的武器，还创造了一套核心思想和工具，为现代复杂系统科学奠定了基础。通过巧妙地利用这一时期出现的计算子状态，我们能够在过去几十年中迅速推进对相互作用系统的理解。

Complexity abounds even in our attempts to understand complexity. The desire to harness the atom for war led to a remarkable web of interacting people, ideas, and technologies. From this web emerged a Promethean bargain, creating not only the most destructive weapons humankind has ever known but also a core set of ideas and tools that have set the stage for the modern science of complex systems. By cleverly harnessing the computational substate that arose during this period, we have been able to rapidly advance our understanding of interacting systems over the past few decades.

事实上，最初设计用于理解原子行为的算法，目前用于推动我们新兴的分析时代，为复杂生命提供了新的视角。自适应代理是宇宙算法舞蹈的一部分，受制于决定其命运的深层力量。

Indeed, algorithms originally designed to understand the behavior of atoms, and currently used to drive our emerging age of analytics, provide a new view of complex life. Adaptive agents are part of a cosmic algorithmic dance, subject to deep forces that determine their fate.

归根结底，我们作为一个社会所面临的挑战中充满了复杂性。以人类面临的任何重大问题为例——气候变化、金融崩溃、生态系统生存、恐怖主义、疾病流行、社会革命——你会发现它们都以复杂系统为基础。来自复杂系统的思想开始重塑我们思考和对待世界的方式。遵循还原论模型的政策——例如，只考虑一家银行持有的证券，而忽略将银行联系在一起的相互联系和相互依赖——注定会失败。只有通过接受更广泛的复杂系统视角，政策制定才能跟上我们日益复杂的世界。

Ultimately, complexity abounds in the challenges that we face as a society. Take any of the major issues confronting humanity—climate change, financial collapse, ecosystem survival, terrorism, disease epidemics, social revolution—and you will see that they have a grounding in complex systems. Ideas from complex systems are starting to reshape the way we think about and act on our world. Policies that follow the reductionist model—for example, considering only the securities held by a single bank while ignoring the interconnections and codependencies that bind banks together—are doomed to fail. It is only by embracing the broader complex-systems perspective that policy making can keep up with our increasingly complex world.

这里探讨的各种思想、理论和观察正在形成一幅重要的新画卷，它将为我们提供看待世界的新视角，并提供推进我们目标的新方法。我们对复杂系统的理解正在形成的画卷本身也受复杂系统规律的支配。因此，它呈现出一种整体的美感、连贯性和实用性，而这些都不是任何单个编织者的意图或能力的一部分。当我们在完全沉默中审视大量存在的复杂性时，构成每根线的各种证据、观察和结论开始淡化为更深的理解。

The various strands of ideas, theories, and observations explored here are forming an important new tapestry that will give us fresh perspectives on our world and provide novel ways to advance our goals. The emerging tapestry of our understanding of complex systems is itself subject to the laws of complex systems. Thus, it is taking on a global beauty, coherence, and utility that were no part of any individual weaver’s intention or ability. The various proofs, observations, and conclusions that form each thread are beginning to fade into a deeper understanding as we look, in perfect silence, at the complexity that abounds.

指数

Index

异速生长，160

allometry, 160

安德森，菲尔，2

Anderson, Phil, 2

蚂蚁

ants

军队，133-134​

army, 133–134

圆磨机，134

circular mill, 134

菌落发现, 127

colony finding, 127

资源决策，133 – 134

resource decisions, 133–134

串联运行，127

tandem running, 127

阿拉伯之春，18，201-202，238​​​

Arab Spring, 18, 201–202, 238

Arrow，Ken，30岁

Arrow, Ken, 30

自动机, 28 , 183 – 193

automata, 28, 183–193

沟通，188-193​

communication, 188–193

 

 

Bak，Per，196

Bak, Per, 196

巴厘岛

Bali

水稻种植，16 – 17，169 – 178，237​​

rice farming, 16–17, 169–178, 237

波索时代, 173

time of poso, 173

水神庙，171 – 173，175

water temples, 171–173, 175

巴雷特，布列塔尼，93岁

Barrett, Brittany, 93

吸引盆地，83 – 84

basins of attraction, 83–84

集市经济学，39 – 44

bazaar economics, 39–44

比克曼，玛德琳，136

Beekman, Madeleine, 136

贝滕科特，路易斯，167

Bettencourt, Luis, 167

博尔赫斯，豪尔赫·路易斯，2，195

Borges, Jorge Luis, 2, 195

布瓦吉吉，穆罕默德，201

Bouazizi, Mohamed, 201

肯尼斯·博尔丁43 岁

Boulding, Kenneth, 43

布莱伯里，诺里斯，208

Bradbury, Norris, 208

布朗，吉姆，161

Brown, Jim, 161

老化，参见马尔可夫链

burn-in, see Markov chain

 

 

细胞自动机，23 – 30，230

cellular automata, 23–30, 230

规则22、29

Rule 22, 29

规则30、24-29​​

Rule 30, 24–29

趋化性，101 – 105，109

chemotaxis, 101–105, 109

城市与国家财富，70 – 71

Cities and the Wealth of Nations, 70–71

克拉克，亚瑟·C，214

Clark, Arthur C., 214

竞争平衡，35 – 45

competitive equilibrium, 35–45

计算机器，参见自动机

computing machines, see automata

芋螺，25 – 28

cone snail, 25–28

芋螺26

Conus omaria, 26

合作，16-17，169-198，237-238​​​​​​​​​

cooperation, 16–17, 169–198, 237–238

 

 

查尔斯·达尔文11 , 21 , 185

Darwin, Charles, 11, 21, 185

德布鲁，杰拉德，30岁

Debreu, Gerard, 30

决策，12 – 13，106 – 108，233 – 235​​​

decision making, 12–13, 106–108, 233–235

公告牌音乐排行榜，118，127，235​

Billboard music charts, 118, 127, 235

分散，12 – 13，113 – 139​

decentralized, 12–13, 113–139

错误，79 – 80，87 – 89，131 – 132​​​

errors, 79–80, 87–89, 131–132

组，22，113-139​​​

group, 22, 113–139

猕猴，131 – 133

macaque monkeys, 131–133

分子，18，100-111​​​

molecular, 18, 100–111

政治初选，235

political primaries, 235

视觉，131

visual, 131

详细平衡，参见马尔可夫过程

detailed balance, see Markov process

多恩，约翰，205 – 206

Donne, John, 205–206

双人竞拍锦标赛，55 – 56

Double Auction Tournament, 55–56

药物鸡尾酒疗法，86 – 87 , 90 – 98

drug cocktails, 86–87, 90–98

癌症化疗，90，92-97​​

cancer chemotherapy, 90, 92–97

 

 

E-迷你, 50 – 51 , 53 , 57 – 59

E-mini, 50–51, 53, 57–59

埃克特，普雷斯珀，207

Eckert, Presper, 207

爱因斯坦，阿尔伯特，206

Einstein, Albert, 206

出现，68，138-139​​​

emergence, 68, 138–139

ENIAC，207 – 208

ENIAC, 207–208

恩奎斯特，布莱恩，161

Enquist, Brian, 161

错误，参见噪音

errors, see noise

金融市场的预期，67 – 68

expectations in financial markets, 67–68

外部性，170-172

externalities, 170–172

 

 

反馈，7 – 9，16，54，58 – 59，61，231 – 233​​​​​​​​​

feedback, 7–9, 16, 54, 58–59, 61, 231–233

费米，恩里科，208

Fermi, Enrico, 208

闪电崩盘，8 – 9 , 47 – 54 , 64 – 67 , 172

flash crash, 8–9, 47–54, 64–67, 172

弗兰克尔·斯坦，207-208

Frankel, Stan, 207–208

 

 

盖尔曼，默里，4，164

Gell-Mann, Murray, 4, 164

一般均衡，31

general equilibrium, 31

遗传算法，184 – 185

genetic algorithm, 184–185

理查德·戈德施密特，185

Goldschmidt, Richard, 185

戈尔曼·拉塞尔，121

Golman, Russel, 121

戈登，黛博拉，133

Gordon, Deborah, 133

群体智力，113 – 135

group intelligence, 113–135

 

 

哈格曼，大卫，121

Hagmann, David, 121

汉尼曼，罗伯特，154

Hanneman, Robert, 154

哈耶克，弗里德里希，37 – 38

Hayek, Friedrich, 37–38

异质性，7 , 10 , 12 , 70 – 73 , 80 , 232 – 233

heterogeneity, 7, 10, 12, 70–73, 80, 232–233

高频交易，54 – 59，61 – 63

high frequency trading, 54–59, 61–63

霍布斯，托马斯，170 – 171

Hobbes, Thomas, 170–171

同质性，参见异质性

homogeneity, see heterogeneity

蜜蜂，13 – 14，229，232​​​

honeybees, 13–14, 229, 232

蜂巢发现，113 – 126

hive finding, 113–126

法定人数，119，122-124​​​

quorum, 119, 122–124

超有机体，113 – 115，235

superorganism, 113–115, 235

群，116 – 123，129​

swarms, 116–123, 129

温度调节，71 – 74

temperature regulation, 71–74

霍伊尔，弗雷德，189

Hoyle, Fred, 189

 

 

智能设计，26

intelligent design, 26

相互作用，6 – 8 , 10 – 11 , 27 – 28 , 228 – 229 , 232

interactions, 6–8, 10–11, 27–28, 228–229, 232

看不见的手，5，30，37，68，231​​​​​

invisible hand, 5, 30, 37, 68, 231

 

 

雅各布斯，简，70 – 71

Jacobs, Jane, 70–71

乔伊斯·詹姆斯79 岁

Joyce, James, 79

 

 

克莱伯，马克斯，160岁

Kleiber, Max, 160

 

 

莱克兰，141 – 151，155​

Lakeland, 141–151, 155

景观，1 – 2，80 – 86，87 – 89​​​

landscape, 1–2, 80–86, 87–89

坚固性，83 – 87,89,94,98​​​​

ruggedness, 83–87, 89, 94, 98

拉蒂，塔尼娅，106岁

Latty, Tanya, 106

洛博，何塞，167

Lobo, José, 167

 

 

多数规则，131、143-145、147、166、238​​​​​​​​

majority rule, 131, 143–145, 147, 166, 238

地图，1 – 2、4、19、32、34、80、82​​​​​​​​​​​

maps, 1–2, 4, 19, 32, 34, 80, 82

市场，8 – 10 , 30 – 39 , 41 – 45 , 47 – 62 , 228 , 231 – 232

markets, 8–10, 30–39, 41–45, 47–62, 228, 231–232

拍卖, 55 – 56 , 136 – 138 , 228

auctions, 55–56, 136–138, 228

自组织，140

self-organization, 140

交易者异质性，74 – 75

trader heterogeneity, 74–75

安德烈·安德烈耶维奇·马尔科夫，212

Markov, Andrey Andreyevich, 212

马尔可夫链，212 – 213，222 – 223

Markov chain, 212–213, 222–223

老化，213，216，220，222 – 224​​​​​

burn-in, 213, 216, 220, 222–224

马尔可夫链蒙特卡洛（MCMC）

Markov chain Monte Carlo (MCMC)

方法，212 – 220，224 – 225​

method, 212–220, 224–225

马尔可夫过程

Markov process

详细余额，214，225

detailed balance, 214, 225

各向异性，212

ergotic, 212

不可约，212

irreducible, 212

常规，212 – 213

regular, 212–213

莫奇利，约翰，207

Mauchly, John, 207

MCMC 算法，请参阅马尔可夫链蒙特卡洛 (MCMC) 方法

MCMC algorithms, see Markov chain Monte Carlo (MCMC) method

大都会，尼克，207 – 210，215，219​

Metropolis, Nick, 207–210, 215, 219

分子智力，100 – 111

molecular intelligence, 100–111

蒙特卡罗方法，208 – 209

Monte Carlo method, 208–209

更多是不同的，22

more is different, 22

 

 

网络，14，16，141-156，235-236​​​​​​​​​

networks, 14, 16, 141–156, 235–236

犯罪，167 – 168，178，236​​​

crime, 167–168, 178, 236

教育，148

education, 148

消息传递，149 – 152

message passing, 149–152

宗教，148

religion, 148

六度分离，151 – 152

six degrees of separation, 151–152

小世界，150

small world, 150

社会政策，201

social policy, 201

神经元，100，129，205-206，208，234​​​​​​​​

neurons, 100, 129, 205–206, 208, 234

中性漂移，190 – 191

neutral drift, 190–191

中性粒细胞，99

neutrophil granulocyte, 99

纽瑟姆，威廉，131

Newsome, William, 131

噪音， 5、7、80、87-88​​​​​​​

noise, 5, 7, 80, 87–88

 

 

奥卡姆，威廉神父，9

Ockham, Father William of, 9

“论科学的准确性”，2

“On Exactitude in Science,” 2

奥本海默，J.罗伯特，205 – 206

Oppenheimer, J. Robert, 205–206

优化，参见搜索

optimization, see search

订单簿，51 – 52，60

order book, 51–52, 60

 

 

普费弗·威廉（Pfeffer, Wilhelm）105 – 106

Pfeffer, Wilhelm, 105–106

政策，十八至十九，173，198，201​

policy, xviii–xix, 173, 198, 201

异质性，73

heterogenity, 73

幂律，158 – 168，196 – 197

power law, 158–168, 196–197

囚徒困境, 178 – 181 , 183

prisoner’s dilemma, 178–181, 183

 

 

随机性，见噪声

randomness, see noise

还原论，2 – 5 , 9 , 12 , 22 , 62 , 228

reductionism, 2–5, 9, 12, 22, 62, 228

代表代理，9 – 10，69 – 70

representative agent, 9–10, 69–70

理查森，刘易斯·弗莱，164 – 165

Richardson, Lewis Fry, 164–165

风险规避，125 – 126

risk aversion, 125–126

罗伯特议事规则，138

Robert’s Rules of Order, 138

罗森布鲁斯，阿里安娜，209

Rosenbluth, Arianna, 209

罗森布鲁斯，马歇尔，209

Rosenbluth, Marshall, 209

 

 

缩放，15 – 16，158 – 167，236​​​

scaling, 15–16, 158–167, 236

城市规模，166 – 168

city size, 166–168

公司规模，166

firm size, 166

寿命，157，160，163​​​

life span, 157, 160, 163

代谢，160 – 163

metabolism, 160–163

人口增长，166，236-237​​

population growth, 166, 236–237

城市化，1​​68

urbanization, 168

战争，164-165​

war, 164–165

文本中的单词，165 – 166

words in a text, 165–166

齐夫定律，165 – 166

Zipf’s law, 165–166

谢林，托马斯，152

Schelling, Thomas, 152

搜索, 80 – 95 , 233

search, 80–95, 233

爬山，80 – 86，88 – 89​

hill climbing, 80–86, 88–89

模拟退火，88 – 89，222

simulated annealing, 88–89, 222

隔离，152 – 155

segregation, 152–155

自组织临界性，17，195-203，238​​

self-organized criticality, 17, 195–203, 238

崩溃，195-198​

collapse, 195–198

玛雅，195、199-201​​​

Maya, 195, 199–201

起义，198

revolts, 198

社会制度，198 – 202

social systems, 198–202

七宗罪，64

seven deadly sins, 64

六西格玛，79 – 80 , 87 , 98

Six Sigma, 79–80, 87, 98

黏菌，106 – 107，109，111​​

slime mold, 106–107, 109, 111

史密斯，亚当，5，30-31，68，231​​​​​

Smith, Adam, 5, 30–31, 68, 231

斯内尔，奥托，106

Snell, Otto, 106

社会运动

social movements

异质性，75 – 77

heterogeneity, 75–77

致命争吵统计164

Statistics of Deadly Quarrels, 164

斯特鲁姆斯基，黛博拉，167

Strumsky, Deborah, 167

供给与需求，31 – 38

supply and demand, 31–38

 

 

泰米叶，伊本，31

Taymiyyah, Ibn, 31

泰勒，奥古斯塔，209

Teller, Augusta, 209

特勒，爱德华，207 – 209

Teller, Edward, 207–209

自适应系统定理，18 – 19，215，217 – 221，223​​​

theorem of adaptive systems, 18–19, 215, 217–221, 223

托尔金，JRR，69

Tolkien, J. R. R., 69

交易算法，52 – 54，57 – 58，77​​

trading algorithms, 52–54, 57–58, 77

三位一体测试，206

Trinity test, 206

米歇尔·图米内洛39 岁

Tumminello, Michele, 39

2008年金融危机，9，64，67，232​​

2008 financial crisis, 9, 64, 67, 232

 

 

乌拉姆，斯坦尼斯瓦夫，5、6、85、208​​

Ulam, Stanislaw, 5, 6, 85, 208

 

 

安东尼·范列文虎克100

van Leeuwenhoek, Antonie, 100

凡勃伦，托尔斯坦，141

Veblen, Thorstein, 141

冯·弗里施，卡尔，13岁

von Frisch, Karl, 13

约翰·冯·诺依曼，5 – 6 , 23 , 207 – 208

von Neumann, John, 5–6, 23, 207–208

 

 

《国富论》第 5 卷，第30 – 31 页

Wealth of Nations, 5, 30–31

韦斯特，杰弗里，161，167

West, Geoffrey, 161, 167

惠特曼，沃尔特，227

Whitman, Walt, 227

 

 

拉尔夫·辛纳（Ralph Zinner），92 岁

Zinner, Ralph, 92

齐夫定律，参见缩放

Zipf’s law, see scaling

Zipf，乔治·金斯利，165

Zipf, George Kingsley, 165

约翰·H·米勒是卡内基梅隆大学社会与决策科学系经济学和社会科学教授，也是圣达菲研究所的外部教员。他住在宾夕法尼亚州匹兹堡。

John H. Miller is a professor of economics and social science at Carnegie Mellon University’s Department of Social and Decision Sciences and an external faculty member of the Santa Fe Institute. He lives in Pittsburgh, Pennsylvania.